Good Turing frequency estimation is a statistical technique for predicting the probability of occurrence of objects belonging to an unknown number of species, given past observations of such objects and their species. In drawing balls from an urn, the objects would be balls and the species would be the distinct colors of the balls finite but unknown in number . After drawing math R text red math red balls, math R text black math black balls and math R text green math green balls, we would ask what is the probability of drawing a red ball, a black ball, a green ball or one of a previously unseen color. Historical background Good Turing frequency estimation was developed by Alan Turing and his assistant I.J. Good as part of their efforts at Bletchley Park to crack Germany German ciphers for the Enigma machine during World War II . Turing at first modeled the frequencies as a binomial distribution , but found it inaccurate. Good developed smoothing algorithms to improve the estimator s accuracy. The discovery was recognized as significant when published by Good in 1953, ref cite journal last Good first I.J. authorlink I.J. Good year 1953 title The population frequencies of species and the estimation of population parameters journal Biometrika volume 40 issue 3&ndash 4 pages 237&ndash 264 doi 10.1093 biomet 40.3 4.237 jstor 2333344 mr 61330 ref but the calculations were difficult so it was not used as widely as it might have been. ref http www.newswise.com articles view 501440 Newsise Scientists Explain and Improve Upon Enigmatic Probability Formula , a popular review of cite journal ... A, Santhanam NP, Zhang J. title Always Good Turing asymptotically optimal probability estimation. pmid ... Good turing frequency estimation without tears ref Primary source claim date February 2012 described ... not described here can be used to specify at what point the switch from no smoothing to linear ... Conference on Computational Learning Theory pp. 1 6 div DEFAULTSORT Good Turing Frequency Estimation ... more details
a posteriori estimation then estimates math theta math as the mode statistics mode of the posterior ... Criticism While MAP estimation is a limit of Bayes estimators under the 0 1 loss function , it is not very representative of Bayesian methods in general. This is because MAP estimates are point estimates ... Hill, 1970 . Harold W. Sorenson, 1980 Parameter Estimation Principles and Problems , Marcel Dekker. Statistics inference Category Estimation theory Category Bayesian inference Category Statistical ... more details
issue is the robust statistics robustness to outlier s ref Robust Estimation and Outlier Detection ... up by explicit statistical models involving the covariance matrix of the variables. Thus the estimation ... of a random sample. Estimation in a general context Given a Sample statistics sample consisting ... the covariance matrix is to treat the estimation of each variance or pairwise covariance ... likelihood estimation for the multivariate normal distribution main Multivariate normal distribution ... normal distribution Estimation of parameters the section on estimation in the article on the normal ... matrix &Sigma . At this point we are using a capital X rather than a lower case x because we are thinking ... i mu d mu T right . math It naturally breaks down into the part related to the estimation of the mean, and to the part related to the estimation of the variance. The first order condition for maximum ... function. Maximum likelihood estimation general case main Maximum likelihood The first order ... theta text MLE right 1 . math Intrinsic covariance matrix estimation Intrinsic expectation Given a Sample ... bias must be generalized to manifolds to make sense of the problem of covariance matrix estimation ... valued point R as math mathrm E mathbf R hat mathbf R stackrel mathrm def exp mathbf R mathrm ... estimation If the sample size n is small and the number of considered variables p is large, the above ..., many methods have been suggested to improve the estimation of the covariance matrix. All ... Approach to Large Scale Covariance Matrix Estimation and Implications for Functional Genomics , Statistical ... covariance References references statistics correlation state expanded DEFAULTSORT Estimation Of Covariance Matrices Category Estimation for specific parameters Category Statistical deviation and dispersion ... more details
Refimprove date December 2009 Motor Unit Number Estimation MUNE is a technique that uses electromyography to estimate the number of motor unit s in a muscle. Principles A motor unit consists of one alpha motoneuron and all the muscle fibres it innervates. Muscles differ in the number of motor units that they contain, and how many muscle fibres are within each unit innervation ratio . In a general sense, muscles that require specificity of movement, such as muscles in charge of eye movement, have fewer fibres per unit, while those that are meant for less specific tasks, such as the calf muscles in charge of jumping, have more. MUNE uses a general formula of Number of motor units compound muscle action potential size divided by the mean surface detected motor unit action potential size The compound muscle action potential CMAP size is found using supramaximal stimulation of the motor nerve to the muscle or muscle group similar to a nerve conduction study . It is recorded using surface electrodes. This is representative of the sum of the surface detected motor unit action potentials from muscles innervated by that nerve . Surface detected motor unit action potential SMUAP size is the contribution of individual motor units. The way of finding the average size of these action potentials depends on the method used, as described below. Methods There are at least six techniques that are currently in use to estimate motor unit numbers. These include incremental stimulation, multi point stimulation method, F response method, spike triggered averaging method and the statistical method. Incremental stimulation is the most illustrative of the concept, and so will be discussed here. According to Henneman s size principle, motor unit recruitment is always in the same order from smallest to largest motor unit. Additionally, the motor unit action potential is an all or none phenomenon .... Instead, the CMAP size is then divided by the mean SMUAP size to get an estimation of the number ... more details
Unreferenced date December 2009 Cost estimation models are mathematical algorithm s or parametric equations used to estimate the costs of a product or project. The results of the models are typically necessary to obtain approval to proceed, and are factored into business plans, budgets, and other financial planning and tracking mechanisms. These algorithms were originally performed manually but now are almost universally computerized. They may be standardized available in published texts or purchased commercially or proprietary, depending on the type of business, product, or project in question. Simple models may use standard spreadsheet products. Models typically function through the input of parameter s that describe the attributes of the product or project in question, and possibly physical resource requirements. The model then provides as output various resources requirements in cost and time. Cost modeling practitioners often have the titles of cost estimators, cost engineers, or parametric analysts. Typical applications include Construction Software Development Manufacturing New product development See also Software development effort estimationEstimation in software engineering Parametric Estimating Estimation Elemental cost planning Cost overrun Parametric model DEFAULTSORT Cost Estimation Models Category Business terms he ru ... more details
In statistical signal processing , the goal of spectral density estimation is to estimation theory estimate the spectral density also known as the power spectrum of a random signal from a sequence of time samples of the signal. Intuitively speaking, the spectral density characterizes the frequency content of the signal. The purpose of estimating the spectral density is to detect any periodicities in the data, by observing peaks at the frequencies corresponding to these periodicities. Techniques Techniques for spectrum estimation can generally be divided into parametric and non parametric methods. The parametric estimation parametric approaches assume that the underlying stationary stochastic process has a certain structure which can be described using a small number of parameters for example, using an Autoregressive moving average model auto regressive or moving average model . In these approaches, the task is to estimate the parameters of the model that describes the stochastic process. By contrast, non parametric statistics non parametric approaches explicitly estimate the covariance or the spectrum of the process without assuming that the process has any particular structure. Following is a partial list of spectral density estimation techniques Periodogram , a classic non parametric technique Autoregressive moving average estimation, based on fitting to an ARMA model Multitaper Least squares spectral analysis , based on least squares fitting to known frequencies References cite book last Porat first B. title Digital Processing of Random Signals Theory & Methods date 1994 publisher Prentice Hall isbn 0130637513 cite book last Priestley first M.B. title Spectral Analysis and Time Series date 1991 publisher Academic Press isbn 0 12 564922 3 Signal processing stub Category Signal processing Category Estimation theory Category Frequency domain analysis fa ... more details
The question of unbiased estimation of a standard deviation arises in statistics mainly as a question in statistical theory . Except in some important situations, outlined later, the task has little relevance to applications of statistics since its need is avoided by standard procedures, such as the use of significance test s and confidence intervals , or by using Bayesian analysis . However, for statistical theory , it provides an exemplar problem in the context of estimation theory which is both simple to state and for which results cannot be obtained in closed form. It also provides an example where imposing the requirement for Bias of an estimator unbiased estimation might be seen as just adding inconvenience, with no real benefit. Background In statistics , the standard deviation is often estimated from a random sample drawn from the population. The most common measure used is the sample standard deviation, which is defined by math s sqrt frac 1 n 1 sum i 1 n x i overline x 2 ,, math ... for the sample variance is known as Bessel s correction , which corrects the bias in the estimation of the sample variance, and some, but not all of the bias in the estimation of the sample standard ... relates to estimation assuming a normal distribution . Bias correction Results for the normal distribution ... of the model. One general approach to estimation would be maximum likelihood . Alternatively .... Effect of autocorrelation serial correlation The material above, to stress the point again, applies ... s 2 math by the quantity in brackets above, then the ACF must be known analytically , not via estimation ... a useful majority of the bias. See also Bessel s correction Estimation of covariance matrices ... estimation of standard deviation. http www.itl.nist.gov div898 handbook pmc section3 pmc32.htm What are Variables Control Charts? NIST PD Statistics DEFAULTSORT Unbiased Estimation Of Standard Deviation Category Estimation for specific parameters Category Summary statistics Category Covariance ... more details
context date December 2010 Maximum likelihood sequence estimation MLSE is a mathematical algorithm to extract useful data out of a noisy data stream. Theory For an optimized detector for digital signals the priority is not to reconstruct the transmitter signal, but it should do a best estimation of the transmitted data with the least possible number of errors. The receiver emulates the distorted channel. All possible transmitted data streams are fed into this distorted channel model. The receiver compares the time response with the actual received signal and determines the most likely signal. In cases that are most computationally straightforward, root mean square deviation can be used as the decision criterion ref G. Bosco, P. Poggiolini, and M. Visintin, Performance Analysis of MLSE Receivers Based on the Square Root Metric, J. Lightwave Technol. 26, 2098&ndash 2109 2008 ref for the lowest error probability. Background Suppose that there is an underlying signal x t , of which an observed ... the observations r t to create a good estimate of x t . Maximum likelihood sequence estimation ... series has the values x t . In contrast, the related method of maximum a posteriori estimation is formally the application of the Maximum a posteriori MAP estimation approach. This is more complex than maximum likelihood sequence estimation and requires a known distribution in Bayesian inference ... normal distribution , the problem of maximum likelihood sequence estimation can be reduced to that of a least ... Estimation pages 362&ndash 364 publisher Cambridge University Press year 2005 isbn 0521837162 ... v35n2a04.pdf Performance evaluation of maximum likelihood sequence estimation receivers in lightwave ..., D., Mahlab, U., and Levy, A. 2008 Channel estimators for maximum likelihood sequence estimation ... External links Cite web title Maximum Likelihood Sequence Estimation of Nonlinear Channels in High ... Estimation Category Telecommunications Category Error detection and correction Category Signal estimation ... more details
Small area estimation is any of several statistical techniques involving the estimation of parameter s for small sub population s, generally used when the sub population of interest is included in a larger statistical survey survey . The term small area in this context generally refers to a small geographical area such as a county. It may also refer to a small domain , i.e. a particular demographic within an area. If a survey has been carried out for the population as a whole for example, a nation or state wide survey , the sample size within any particular small area may be too small to generate accurate estimates from the data. To deal with this problem, it may be possible to use additional data such as census records that exists for these small areas in order to obtain estimates. One of the more common small area Linear regression models in use today is the nested area unit level regression model , first used in 1988 to model corn and soybean crop areas in Iowa. The initial survey data, in which farmers reported the area they had growing either corn or soybeans, was compared to estimates obtained from satellite mapping of the farms. The final model resulting from this for unit farm j in country i is math y ij x ij beta mu i epsilon ij , math , where y denotes the reported crop area, math beta , math is the regression coefficient, x is the farm level estimate for either corn or soybean usage from the satellite data and math mu , math represents the county level effect of any area characteristics that haven t been accounted for. References G.E Battese, R.M Harter & W.A Fuller. An error component model for prediction of county crop areas using survey and satellite data , Journal of the American Statistical Association, 83, 28 36. M Ghosh, J.N.K. Rao. Small area estimation An appraisal , Statistical Science, vol 9, no.1 1994 , 55 76. Danny Pfefferman. Small area estimation ... Rao 2003 , Small area estimation , Wiley. Category Estimation theory ... more details
In statistics , a stochastic kernel estimate is an estimate of the transition function of a usually discrete time stochastic process . Often, this is an estimate of the conditional density function obtained using kernel density estimation . The estimated conditional distribution can then be used to derive estimates of other properties of the stochastic process , such as the stationary distribution . External links http econpapers.repec.org scripts redir.pl?u http 3A 2F 2Fwww.ibmecsp.edu.br 2Fpesquisa 2Fdownload.php 3Frecid 3D3115 h repec ibm ibmecp wpe 88 Conditional Stochastic Kernel Estimation by Nonparametric Methods Laurini, M rcio P. & Valls Pereira, Pedro L. Category Stochastic processes Category Non parametric statistics Statistics stub de bergangswahrscheinlichkeit it Probabilit di transizione ... more details
Unreferenced date December 2009 Context date October 2009 Estimation of a Rasch model is used to estimate the parameters of the Rasch model . Various techniques are employed to estimate the parameters from matrices of response data. The most common approaches are types of maximum likelihood estimation, such as joint and conditional maximum likelihood estimation. Joint maximum likelihood JML equations are efficient, but inconsistent for a finite number of items, whereas conditional maximum likelihood CML equations give consistent and unbiased item estimates. Person estimates are generally thought to have bias of an estimator bias associated with them, although weighted likelihood estimation methods for the estimation of person parameters reduce the bias. Rasch model The Rasch model for dichotomous data takes the form math Pr X ni 1 frac exp beta n delta i 1 exp beta n delta i , math where math beta n math is the ability of person math n math and math delta i math is the difficulty of item math i math . Joint maximum likelihood Let math x ni math denote the observed response for person n on item i . The probability of the observed data matrix, which is the product of the probabilities of the individual responses, is given by the likelihood function math Lambda frac prod n prod i exp x ni beta n delta i prod n prod i 1 exp beta n delta i . math The log likelihood function is then math log Lambda sum n N beta n r n sum i I delta i s i sum n N sum i I log 1 exp beta n delta i math where math r n sum i I x ni math is the total raw score for person n , math s i sum n N x ni math is the total raw score for item i , N is the total number of persons and I is the total number of items ... 3 . math Estimation algorithms Some kind of expectation maximization algorithm is used in the estimation of the parameters of Rasch models. Algorithms for implementing Maximum Likelihood estimation commonly ... also Expectation maximization algorithm Rasch model DEFAULTSORT Rasch Model Estimation Category Psychometrics ... more details
spacing estimation may be successful. Apart from its use in pure mathematics and statistics, the trial ... estimation , but with more robust properties for various classes of problems. There are certain ... is an unknown parameter to be estimation estimated , let x sub 1 sub , , x sub n sub be the corresponding ... the maximum spacing estimator. Example 1 Image Spacing Estimation plot for MSE example.svg thumb ... both likelihood and spacing estimation. The values for which both likelihood and spacing are maximized ... the estimates of the other parameters inconsistent. Note that there is no inflection point ... R84 The consistency of maximum spacing estimation holds under much more general conditions than for maximum ... last3 Gy rfi first3 L. last4 van der Meulen first4 E.C. year 1997 title Nonparametric entropy estimation .... An estimation method related to the maximum likelihood method journal Scandinavian Journal of Statistics ... first3 Alex year 2005 title The maximum spacing estimation for multivariate observations journal Journal ... year 2006 title Time series and related topics in memory of Ching Zong Wei chapter A note on the estimation ... 0702830v1 ref harv refend Statistics good article DEFAULTSORT Maximum Spacing Estimation Category Estimation theory Category Mathematical modeling ... more details
Minimum distance estimation MDE is a statistical method for fitting a mathematical model to data, usually the Empirical distribution function empirical distribution . Definition Let math displaystyle X 1, ldots,X n math be an Independent and identically distributed random variables independent and identically distributed iid Random variable random Random sample sample from a Statistical population population with Cumulative distribution function distribution math F x theta colon theta in Theta math and math Theta subseteq mathbb R k k geq 1 math . Let math displaystyle F n x math be the empirical distribution function based on the sample. Let math hat theta math be an estimator for math displaystyle theta math . Then math F x hat theta math is an estimator for math displaystyle F x theta math . Let math d cdot, cdot math be a Functional mathematics functional returning some measure of Distance General case distance between the two Dependent and independent variables Mathematics arguments . The functional math displaystyle d math is also called the criterion function. If there exists a math ... math . Statistics used in estimation Most theoretical studies of minimum distance estimation, and most .... Below are some examples of statistical tests that have been used for minimum distance estimation ... of minimum distance estimation is related to that for the asymptotic distribution of the corresponding ... covariance matrices of the parameter estimates. See also Maximum likelihood estimation Maximum spacing estimation inline date October 2011 References reflist refbegin Boos, D.D. 1982 . Minimum Anderson Darling Estimation . Communications in Statistics, Part A Theory and Methods, 11 24 , 2747 ... and robust estimation . Journal of the American Statistical Association, 75, 616&ndash 624. cite journal ... 2008 09 24 refend Statistics inference DEFAULTSORT Minimum distance estimation Categories Category Estimation theory Category Statistical distance measures Category Mathematical modeling ... more details
Quantitative precipitation estimation or QPE is a method of approximating the amount of Precipitation meteorology precipitation that has fallen at a location or across a region. Maps of the estimated amount of precipitation to have fallen over a certain area and time span are compiled using several different data sources including manual and automatic field observations and radar and satellite data. This process is undertaken every day across the United States at Weather Forecast Offices WFOs run by the National Weather Service NWS . A number of different algorithms can be used to estimate precipitation amounts from data collected by radar. ref cite web url http www.cimms.ou.edu kscharf pol qpe.html title Quantitative Precipitation Estimation QPE Algorithms publisher CIMMS, University of Oklahoma accessdate 2010 04 14 ref Research in the fields of QPE and Quantitative Precipitation Forecast quantitative precipitation forecasting QPF is ongoing. References reflist Category Meteorology Category Hydrology Meteorology stub ... more details
About evolutionary computation methods on estimating probability distribution s density estimation Context date September 2009 Citations missing date January 2008 Image Eda mono variant gauss iterations.svg thumb 350px Estimation of distribution algorithm. For each iteration i , a random draw is performed for a population P in a distribution PDu . The distribution parameters PDe are then estimated using the selected points PS . The illustrated example optimizes a continuous objective function f X with a unique optimum O . The sampling following a normal distribution N concentrates around the optimum as one goes along unwinding algorithm. Estimation of distribution algorithms EDAs , sometimes called probabilistic model building genetic algorithms PMBGAs , are stochastic optimization methods that guide the search for the optimum by building and sampling explicit probabilistic models of promising candidate solutions. Optimization is viewed as a series of incremental updates of a probabilistic model, starting with the model encoding the uniform distribution over admissible solutions and ending with the model that generates only the global optima. EDAs belong to the class of evolutionary algorithms . The main difference between EDAs and most conventional evolutionary algorithms is that evolutionary ... Estimation of Multivariate Normal Algorithm EMNA Mutual Information Maxminization for Input Clustering ... Optimization Algorithm BOA Estimation of Bayesian Networks Algorithm EBNA Stochastic hill climbing ... Program Evolution PIPE Estimation of Gaussian Networks Algorithm EGNA References Citation style date September 2009 Larra aga, Pedro & Lozano, Jose A. Eds. . Estimation of distribution algorithms A new ..., P. Inza, I. & Bengoetxea, E. Eds. . Towards a new evolutionary computation. Advances in estimation ... probabilistic modeling From algorithms to applications publisher Springer . DEFAULTSORT Estimation ... stub es Algoritmo de estimaci n de distribuci n fr Algorithme estimation de distribution pt Algoritmos ... more details
A comparison of notable Software development effort estimation software. PLEASE NOTE Please only place entries here that describe development estimation software meaning they can can do at least either Schedule or Cost estimate. If you have questions, use the talk page. Please try to keep entries in alphabetical order. Thanks. class wikitable sortable style text align center width 100 Software Schedule estimate Cost estimate Software development effort estimation Cost Models Input Report Output Format Programming language Supported Programming Languages Computing platform Platforms Software license License AFCAA REVIC ref AFCAA Revic 9.2 manual http sites.google.com site revic92 Revic memorial site ref yes yes REVIC Source lines of code KLOC , Scale Factors, Cost Drivers proprietary, Text any DOS Free Costar ref Costar overview http www.softstarsystems.com factpage.htm SoftStarSystems site ref yes yes COCOMO II, COCOMO 81, REVIC Source lines of code KLOC , Scale Factors, Cost Drivers proprietary, Excel, CSV any Windows Commercial ProjectCodeMeter ref ProjectCodeMeter Documentation http www.projectcodemeter.com Project Code Meter site ref yes yes Weighted Micro Function Points , COCOMO II 2000, COCOMO 81, REVIC Automatic Source Scanning, Cost Drivers HTML, Excel, CSV C, C , C , J , Java, PHP, Objective C, JavaScript, UnrealEngine script, Flash ActionScript, DigitalMars D Windows Commercial SEER SEM Seer for Software ref Seer for Software Datasheet http www.galorath.com index.php products software C5 Galorath site ref yes yes SEER SEM Source lines of code SLOC , Function points , use cases, bottoms up, object, features proprietary, Excel, Microsoft Project, IBM Rational, Oracle Crystal Ball any Windows Commercial SystemStar ref SystemStar overview http www.softstarsystems.com ... use References Reflist See also Software Sizing Software metric Software development effort estimation Software parametric models Cost estimation models Category Software project management Category Software ... more details
title Eigenvalue Estimation author Dieter van Melkebeek date 2010 09 27 quantum computing DEFAULTSORT Quantum Phase Estimation Algorithm Category Quantum algorithms fr Algorithme d estimation de phase ... more details
The maximum entropy method applied to spectral density estimation . The overall idea is that the maximum entropy rate stochastic process that satisfies the given constant autocorrelation and variance constraints, is a linear Gauss Markov process with i.i.d. zero mean, Gaussian function Gaussian input. Method description The maximum entropy rate, strongly stationary stochastic process math x i math with autocorrelation sequence math R xx k , k 0,1, dots P math satisfying the constraints math R xx k alpha k math for arbitrary constants math alpha k math is the math P math th order, linear Markov chain of the form math x i sum k 1 P a k x i k y i math where the math y i math are zero mean, i.i.d. and normally distributed of finite variance math sigma 2 math . Spectral estimation Given the math a k math , the square of the absolute value of the transfer function of the linear Markov chain model can be evaluated at any required frequency in order to find the power spectrum of math x i math . References Cover, T. and Thomas, J. 1991 Elements of Information Theory, John Wiley and Sons, Inc. External links kSpectra Toolkit for Mac OS X from http www.spectraworks.com SpectraWorks. Category Entropy Category Information theory Category Signal processing Category Time series analysis ... more details
In econometrics , Prais Winsten estimation is a procedure meant to take care of the Autocorrelation serial correlation of type Autoregressive model Example An AR.281.29 process AR 1 in a linear model . It is a modification of Cochrane Orcutt estimation in the sense that it does not lose the first observation and leads to more efficiency statistics efficiency as a result. Theory Consider the model math y t alpha X t beta varepsilon t, , math where math y t math is the time series of interest at time t , math beta math is a Vector geometry vector of coefficients, math X t math is a matrix of explanatory variable s, and math varepsilon t math is the error term . The error term can be serial correlation serially correlated over time math varepsilon t rho varepsilon t 1 e t, rho 1 math and math e t math is a white noise. In addition to the Cochrane Orcutt procedure transformation, which is math y t rho y t 1 alpha 1 rho beta X t rho X t 1 e t. , math for t 2,3,...,T, Prais Winsten procedure makes a reasonable transformation for t 1 in the following form math sqrt 1 rho 2 y 1 alpha sqrt 1 rho 2 left sqrt 1 rho 2 X 1 right beta sqrt 1 rho 2 e 1. , math Then the usual linear least squares least squares estimation is done. Estimation procedure To do the estimation in a compact way it is directive to look at the auto covariance function of the error term considered in the model above math mathrm cov varepsilon t, varepsilon t h frac rho h 1 rho 2 , text for h 0, pm 1, pm 2, dots , . math Now is easy to see that the variance covariance, math mathbf Omega math , of the model is math mathbf Omega begin bmatrix frac 1 1 rho 2 & frac rho 1 rho 2 & frac rho 2 1 rho 2 & cdots & frac rho T 1 1 rho 2 8pt frac rho 1 rho 2 & frac 1 1 rho 2 & frac rho 1 rho 2 & cdots & frac rho T 2 1 rho 2 8pt ... estimation procedure sketched above is helpful. The inverse of math mathbf Omega math can be decomposed ... procedure maybe used to make the estimation feasible. See Cochrane Orcutt estimation . More ... more details
Cochrane Orcutt estimation is a procedure in econometrics , which adjusts a linear model for serial correlation in the error term. It is named after statistician s D. Cochrane and G. H. Orcutt, who worked in the Department of Applied Economics, Cambridge U.K. . Theory Consider the model math y t alpha X t beta varepsilon t, , math where math y t math is the time series of interest at time t , math beta math is a Vector geometry vector of coefficients, math X t math is a matrix of explanatory variable s, and math varepsilon t math is the error term . The error term can be serial correlation serially correlated over time math varepsilon t rho varepsilon t 1 e t, rho 1 math . The Cochrane Orcutt procedure transforms the model math y t rho y t 1 alpha 1 rho beta X t rho X t 1 e t. , math Then the sum of squared residuals math e t 2 math is minimized with respect to math alpha, beta math , conditional on math rho math . Restrictions If math rho math is not known, then it is estimated by first getting the residuals of the model math hat varepsilon t math and regressing math hat varepsilon t math on math hat varepsilon t 1 math , leading to an estimate of math rho math and making the transformed regression sketched above feasible. This procedure can be done until in consecutive steps of estimating the correlation coefficient no substantial change is observed. Note that this procedure is designed for an AR 1 error term structure and you would lose the first observation, which might be important for small samples. See also Prais Winsten transformation Newey West estimator Literature Cochrane and Orcutt. 1949. Application of least squares regression to relationships containing autocorrelated error terms . Journal of the American Statistical Association 44, pp 32 61 DEFAULTSORT Cochrane Orcutt Estimation Category Econometrics Category Time series analysis Category Regression with time series structure ... more details
Infobox Film name Blue Film Estimation image Blue Film Estimation.jpg image size caption Theatrical poster for Blue Film Estimation 1968 director Kan Mukai ref cite web url http www.jmdb.ne.jp 1968 cr000730.htm title accessdate 2010 02 19 language Japanese publisher Japanese Movie Database ref producer writer Atsushi Yamatoya narrator starring Mari Nagisa br Kemi Ichiboshi ref name poster br Norihiro tani music cinematography Shir Suzuki editing distributor Mukai Productions br Nihon Geijutsu Kyokai br Wakamatsu Productions br Kant Movies released March 1968 runtime 69 minutes country Japan language Japanese budget gross preceded by followed by nihongo Blue Film Estimation Aoi firumu shinasadame is a 1968 in film 1968 Japan ese pink film directed by Kan Mukai . It is in the Part color format which was common with Pink films in the late 1960s and early 1970s before Nikkatsu s entry into the genre with their Roman Porno films. Synopsis The film depicts the plight of a female office worker whose boss introduces to the world of pornographic films. ref name Weisser cite book last Weisser first Thomas coauthors Yuko Mihara Weisser title Japanese Cinema Encyclopedia The Sex Films year 1998 page 70 publisher Vital Books Asian Cult Cinema Publications location Miami isbn 1 889288 52 7 ref Cast Mari Nagisa as Maya typist ref name Weisser ref name World Filmography cite book last Cowie first Peter editor title World Filmography 1967 year 1977 publisher Oak Tree Publications location London isbn 0 498015 69 6 page 355 chapter Japan ref Kemi Ichiboshi ref name poster From film poster ref Norihiro tani as Kunio Mitsugu Fujii Risa Minakami Background Director Kan Mukai often capitalized on controversy to boost the publicity surrounding the release of his films. In the case of Blue Film Estimation , the advertising campaign emphasizing the appearance of mainstream actress Mitsugu Fujii in this pink film created enough public notice to make the film a success ... more details
cleanup date July 2009 Location estimation in wireless sensor networks is the problem of Estimation theory estimating the location of an object from a set of noisy measurements, when the measurements are acquired in a distributed manner by a set of sensors. Motivation Many civilian and military applications require monitoring that can identify objects in a specific area, such as monitoring the front entrance of a private house by a single camera. Monitored areas that are large relative to objects of interest often require multiple sensors e.g., infra red detectors at multiple locations. A centralized observer or computer application monitors the sensors. The communication to Power and bandwidth requirements call for efficient design of the sensor, transmission, and processing. The CodeBlue system http www.eecs.harvard.edu mdw proj codeblue of Harvard university is an example where a vast number of sensors distributed among hospital facilities allow staff to locate a patient in distress. In addition, the sensor array enables online recording of medical information while allowing the patient ... processing the data applies a pre defined estimation rule math hat theta f m 1 x 1 , cdot,m N x N math ... , cdot,m N x N math are designed to minimize estimation error. For example minimizing the mean squared ... estimation for wireless sensor Networks part I Gaussian case journal IEEE Trans. On Sig. Proc. date ... knowledge about the approximated location of math theta math . A coarse estimation can be used to overcome ... Quan title Universal decentralized estimation in a bandwidth constrained sensor network journal IEEE ... estimation for wireless sensor networks part II unknown probability density function journal IEEE ... math N 2 math sensors use math m B x I x tau 2 math . The processing center estimation rule is generated ... in ref cite journal last Xiao first Jin Jun coauthors Andrea J. Goldsmith title Joint estimation ... Wireless Sensor Network Category Estimation theory Category Detection theory Category Wireless sensor ... more details
Recursive Bayesian estimation , also known as a Bayes filter , is a general probabilistic approach for density estimation estimating an unknown probability density function recursively over time using incoming measurements and a mathematical process model. In robotics A Bayes filter is an algorithm used in computer science for calculating the probabilities of multiple beliefs to allow a robot to infer its position and orientation. Essentially, Bayes filters allow robots to continuously update their most likely position within a coordinate system, based on the most recently acquired sensor data. This is a recursive algorithm. It consists of two parts prediction and innovation. If the variables are linear and Normal Distribution normally distributed the Bayes filter becomes equal to the Kalman filter . In a simple example, a robot moving throughout a grid may have several different sensors that provide it with information about its surroundings. The robot may start out with certainty that it is at position 0,0 . However, as it moves farther and farther from its original position, the robot has continuously less certainty about its position using a Bayes filter, a probability can be assigned to the robot s belief about its current position, and that probability can be continuously updated from additional sensor information. Model The true state math x math is assumed to be an unobserved Markov process , and the measurements math z math are the observed states of a Hidden Markov Model HMM . The following picture presents a Bayesian Network of a HMM. Image HMM Kalman Filter Derivation.svg Hidden Markov Model center Because of the Markov assumption, the probability of the current true state given the immediately previous one is conditionally independent of the other earlier states ... Sequential Bayesian filtering Sequential Bayesian filtering is the extension of the Bayesian estimation ... Category Bayesian statistics Category Estimation theory Category Nonlinear filters Category Linear ... more details
Traffic estimation and prediction systems TrEPS have the potential to improve traffic conditions and reduce travel delays by facilitating better utilization of available capacity. These systems exploit currently available and emerging computer, communication, and control technologies to monitor, manage, and control the transportation system. They also provide various levels of traffic information and trip advisory to system users, including many ITS service providers, so that travelers can make timely and informed travel decisions. Need for TrEPS Nofootnotes date April 2008 The success of ITS technology deployments is heavily dependent on the availability of timely and accurate estimates of prevailing and emerging traffic conditions. As such, there is a strong need for a traffic prediction system . The needed system is to utilize advanced traffic models to analyze data, especially real time traffic data, from different sources to estimate and predict traffic conditions so that proactive Advanced Traffic Management System s ATMS and Advanced Traveler Information Systems ATIS strategies can be implemented to meet various traffic control, management, and operation objectives. Research USA In USA , the Federal Highway Administration FHWA R&D initiated a Dynamic Traffic Assignment DTA research project in 1994 to meet the need for a traffic prediction system and to help address complex traffic control and management issues in the dynamic ITS environment. The main objective of this research is to develop a deployable real time Traffic Estimation and Prediction System TrEPS to meet the information need in the ITS context. In October 1995, two parallel research contracts were awarded to Massachusetts Institute of Technology MIT and the University of Texas at Austin UTX with a follow up development and support at the University of Maryland, College Park University of Maryland UMD ..., with a traffic estimation and prediction tool, which uses historical traffic data and real time feeds ... more details
Various methods and tools are involved in stellar age estimation , an attempt to identify within reasonable degrees of confidence what the age of a star is. These methods include stellar stellar evolution evolutionary models , membership in a given star cluster or star system system , fitting the star with the standard stellar classification spectral and luminosity classification system , and the presence of a protoplanetary disk , among others. Nearly all of the methods of determining age require knowledge of the mass of the star, which can be known through various methods. No individual method can provide accurate results for all types of stars. ref name astroreview cite journal doi 10.1146 annurev astro 081309 130806 title The Ages of Stars year 2010 last1 Soderblom first1 David R. journal Annual Review of Astronomy and Astrophysics volume 48 pages 581 ref Luminosity increase and the Hertzsprung Russell diagram As stars grow older, their luminosity increases at an appreciable rate. ref name theuniverse 2012 cite web title Worst Days on Planet Earth url http www.history.com shows the universe episodes season 6 work The History Channel website publisher The History Channel accessdate 7 March 2012 ref Given the mass of the star, one can use this rate of increase in luminosity in order to determine the age of the star. This method only works for calculating stellar age on the main sequence , because in advanced evolutionary stages of the star, such as the red giant stage, the standard relationship for the determination of age no longer holds. However, when one can observe a red giant star with a known mass, one can calculate the main sequence lifetime, ref name swin main seq cite web title Main Sequence Lifetime url http astronomy.swin.edu.au cosmos M Main Sequence Lifetime work Swinburne Astronomy Online publisher Swinburne University of Technology accessdate 7 March 2012 ... can estimate the age of the Cepheid variable. Exceptional stellar properties which allow for an estimation ... more details
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