The paper considers the problem of modelling and analysing a time series of measurements which take the form of unit two-dimensional vectors. Several general classes of existing and new models are studied in terms of ...
详细信息
The paper considers the problem of modelling and analysing a time series of measurements which take the form of unit two-dimensional vectors. Several general classes of existing and new models are studied in terms of feasibility and flexibility. An approach is recommended which uses two of these classes, and which takes advantage of several standard time series algorithms that are available in modern software packages. An application is given to the analysis of a series of data on wind directions.
Often sports announcers, particularly in baseball, provide the listener with exaggerated information concerning a player's performance. For example, we may be told that Dave Winfield, a popular baseball player, ha...
详细信息
Often sports announcers, particularly in baseball, provide the listener with exaggerated information concerning a player's performance. For example, we may be told that Dave Winfield, a popular baseball player, has hit safely in 8 of his last 17 chances (a batting average of .471). This is biased, or selected information, as the “17” was chosen to maximize the reported percentage. We model this as observing a maximum success rate of a Bernoulli process and show how to construct the likelihood function for a player's true batting ability. The likelihood function is a high-degree polynomial, but it can be computed exactly. Alternatively, the problem yields to solutions based on either the em algorithm or Gibbs sampling. Using these techniques, we compute maximum likelihood estimators, Bayes estimators, and associated measures of error. We also show how to approximate the likelihood using a Brownian motion calculation. We find that although constructing good estimators from selected information is difficult, we seem to be able to estimate better than expected, particularly when using prior information. The estimators are illustrated with data from the 1992 Major League Baseball season.
In this paper towed array data are investigated. The estimation of both the number of signals and the model parameters are considered. Recursive estimation of the parameters is performed by stochastic approximation an...
详细信息
In this paper towed array data are investigated. The estimation of both the number of signals and the model parameters are considered. Recursive estimation of the parameters is performed by stochastic approximation and a recursive em algorithm. The proposed algorithms are applied to towed array data measured in the Baltic Sea.
The em algorithm is a popular iterative method for estimating parameters in the latent class model where at each step the unknown parameters can be estimated simply as weighted sums of some latent proportions. The alg...
详细信息
The em algorithm is a popular iterative method for estimating parameters in the latent class model where at each step the unknown parameters can be estimated simply as weighted sums of some latent proportions. The algorithm may also be used when some parameters are constrained to equal given constants or each other. It is shown that in the general case with equality constraints, the em algorithm is not simple to apply because a nonlinear equation has to be solved. This problem arises, mainly, when equality constraints are defined over probabilities in different combinations of variables and latent classes. A simple condition is given in which, although probabilities in different variable-latent class combinations are constrained to be equal, the em algorithm is still simple to apply.
Abstract. A hidden Markov regime is a Markov process that governs the time or space dependent distributions of an observed stochastic process. We propose a recursive algorithm for parameter estimation in a switching a...
详细信息
Approximate maximum likelihood and related estimation techniques for source location estimation are investigated. An extended model of the spectral density matrix of the sensor array output for coherent sources (multi...
详细信息
Approximate maximum likelihood and related estimation techniques for source location estimation are investigated. An extended model of the spectral density matrix of the sensor array output for coherent sources (multipath propagation) is introduced. We show that the em algorithm can be successfully appplied for this special case of practical importance. In contrast to [2], the em iteration scheme is derived by exploiting that the distribution type of the finite Fourier- transformed sensor outputs belongs to the exponential family. This approach requires neither the additional noise parameters used in [2] nor an alternating step by step optimization of spectral and source location parameters. Finally, we investigate the co-called approximate dual maximum likelihood estimate.
This is a critical evaluation of the rules for coding and scoring of missing responses to multiple-choice items in educational tests. The focus is on tests in which the test-takers have little or no motivation; in suc...
详细信息
This is a critical evaluation of the rules for coding and scoring of missing responses to multiple-choice items in educational tests. The focus is on tests in which the test-takers have little or no motivation; in such tests omitting and not reaching (as classified by the currently adopted operational rules) is quite frequent. Data from the 1991 NAEP Reading Assessment of 17-year-olds are used in analyses and illustrative examples. Alternative rules for scoring based on hypothesized behaviour of the test-takers are proposed.
A method is provided for computing the standard errors for estimated parameters of a normal mixture model fitted to grouped truncated data. An estimate of the information matrix is obtained in terms of quantities comp...
详细信息
New finite-dimensional filters and smoothers are obtained that are related to the Wonham filter of a noisily observed Markov chain, In particular, finite-dimensional, recursive filters and smoothers are given for the ...
详细信息
New finite-dimensional filters and smoothers are obtained that are related to the Wonham filter of a noisily observed Markov chain, In particular, finite-dimensional, recursive filters and smoothers are given for the number of jumps from state i to state j, for the occupation time of state i, and for a stochastic integral related to the drift in the observations These filters allow easy application of the em algorithm for the estimation of the parameters or the Markov chain and observation process.
Estimating the times until incidences of bivariate progressive processes that are categorical is a common problem in ophthalmology, audiology, pulmonary medicine, and other fields of medical research. We consider stud...
详细信息
Estimating the times until incidences of bivariate progressive processes that are categorical is a common problem in ophthalmology, audiology, pulmonary medicine, and other fields of medical research. We consider study designs in which diagnoses of subject's bivariate status are performed repeatedly across time and when diagnosis is subject to error. In such situations, error confounds the interpretation of the time until an event. A composite model is proposed for parameterizing both the incidence and error distributions, which allows for correlation between sites with respect to both incidence and diagnostic error. An em algorithm is described for this model, which allows categorical covariates for both incidence and error. The methodology is applied to two examples. The first represents a situation in which bivariate incidence and error can reasonably be assumed symmetric: prospective data concerning the development of ocular lens opacities in a large pharmaceutical clinical trial. The second example represents a situation in which bivariate incidence and error may not be symmetric: clinical evaluations of sexual maturation status with respect to two different anatomical indices in the Cooperative Study of Sickle Cell Disease. The methodology described in this paper is used, in each case, to estimate incidence, characterize error rates, and assess bivariate correlations.
暂无评论