Showing papers on "Likelihood principle published in 1979"
Posted Content•
TL;DR: In this paper, the joint maximum likelihood estimator of the structural parameters is not consistent as the number of groups increases, with a fixed number of observations per group, and a conditional likelihood function is maximized, conditional on sufficient statistics for the incidental parameters.
Abstract: In data with a group structure, incidental parameters are included to control for missing variables. Applications include longitudinal data and sibling data. In general, the joint maximum likelihood estimator of the structural parameters is not consistent as the number of groups increases, with a fixed number of observations per group. Instead a conditional likelihood function is maximized, conditional on sufficient statistics for the incidental parameters. In the logit case, a standard conditional logit program can be used. Another solution is a random effects model, in which the distribution of the incidental parameters may depend upon the exogenous variables.
2,338 citations
01 Jan 1979
TL;DR: The expected distribution of classes in a final classification map can be used to improve classification accuracies by modifying the maximum likelihood decision rule employed in a Bayesian-type classifier to calculate posteriori probabilities of class membership.
405 citations
TL;DR: In this paper, the robustness property of the preliminary test estimator when the assumed restraints may not hold was analyzed for a general multi-sample parametric model and compared with the parallel expressions for the unrestricted and restricted maximum likelihood estimators.
Abstract: Along with the asymptotic distribution, expressions for the asymptotic bias and asymptotic dispersion matrix of the preliminary test maximum likelihood estimator for a general multi-sample parametric model (when the null hypothesis relating to the restraints on the parameters may not hold) are derived and compared with the parallel expressions for the unrestricted and restricted maximum likelihood estimators. This study reveals the robustness property of the preliminary test estimator when the assumed restraints may not hold.
135 citations
TL;DR: In this article, it was shown that with probability one MLEs for the parameters of the von Mises-Fisher matrix distribution exist and are unique, both in the case where the parameter matrix has known rank and in the unrestricted case.
Abstract: It has been conjectured by Khatri and Mardia that with probability one MLEs for the parameters of the von Mises-Fisher matrix distribution exist and are unique. We prove that, except for small sample sizes, this conjecture is true, both in the case where the parameter matrix has known rank and in the unrestricted case. The corresponding result for the matrix Bingham distribution is proven also.
109 citations
TL;DR: In this paper, a bias correction using higher derivatives of the log likelihood is shown to be effective in a simulation study of a medical diagnosis problem, where the procedure is illustrated in a medical simulation problem.
Abstract: Maximum likelihood estimates of the parameters for logistic discrimination show considerable bias in small samples, Adjustment by a bias correction using higher derivatives of the log likelihood is shown to be effective in a simulation study. The procedure is illustrated in a medical diagnosis problem.
90 citations
TL;DR: In this paper, the authors derived an expression for the exact likelihood function of a stationary process generated by a vector autoregressive-moving average model using concentrated maximum likelihood techniques, and in the process of deriving the likelihood function, a closed form expression for covariance function of the process in terms of the coefficients of the model is derived.
Abstract: SUMMARY By making use of the properties of tensor products, this paper describes the derivation of an expression for the exact likelihood function of a stationary process generated by a vector autoregressive-moving average model using concentrated maximum likelihood techniques. Furthermore, in the process of deriving the likelihood function, a closed form expression for the covariance function of the process in terms of the coefficients of the model is derived.
68 citations
TL;DR: In this paper, the application of the principle of maximum likelihood to the analysis of fatigue test results, including run-out, is described The particular method used is that developed by Edwards, called "Support" The paper describes the use of this method in determining means and standard deviations for test results.
47 citations
38 citations
TL;DR: In this paper, it is argued that logic requires a test of discrimination to be one-tailed and a significance test for a non-nested hypothesis to be two-tailed.
37 citations
TL;DR: In this article, the maximum likelihood estimators of the parameters and the associated large sample covariance matrix are derived for a censored sample from a bivariate normal distribution consisting of the first k of n-order statistics of one variable and the induced order statistics of the other variable.
Abstract: SUMMARY For a censored sample from a bivariate normal distribution consisting of the first k of n order statistics of one variable and the induced order statistics of the other variable, the maximum likelihood estimators of the parameters and the associated large sample covariance matrix are derived. The likelihood ratio test for independence is also given and its power properties studied. These methods are useful in selection problems or in life testing situations in which concomitant variates are observable only for the uncensored primary variates.
28 citations
TL;DR: In this paper, the authors considered the maximum likelihood estimation of the five parameters of a linear structural relationship y = α + βx when α is known, and the parameters are β, the two variances of observation errors on x and y, the mean and variance of x.
Journal Article•
TL;DR: In this paper, a procedure for representing a set of grouped data by a mixture of two normal distributions and two Weibull distributions, using maximum likelihood estimates, is described. But the procedure is not suitable for large sets of data.
Abstract: Computer programs are given for a procedure for representing a set of grouped data by 1). a mixture of two normal distributions, and 2). a mixture of two Weibull distributions, using maximum likelihood estimates...
TL;DR: In this article, a third-order optimum property of the maximum likelihood estimator is extended to not necessarily symmetric loss functions under an appropriate restriction on the class of competing estimators.
TL;DR: The program which is written in FORTRAN calculates maximum likelihood estimates of gene frequencies and their standard errors in each population and in the populations taken together.
TL;DR: In this paper, the authors used the method of scoring to obtain maximum likelihood estimates of the parameters in the White and Clark learning hierarchy validation model, and the hypothesis of inclusion was tested.
Abstract: The method of scoring is used to obtain maximum likelihood estimates of the parameters in the White and Clark learning hierarchy validation model. From the estimate of the proportion of the population possessing only the superordinate skill in a pair of hierarchical skills, and its variance, the hypothesis of inclusion is tested. An illustrative example of the procedure is given.
TL;DR: In this paper, the authors describe maximum likelihood procedures for the Rotterdam model when the model is formulated in relative prices and under the constraints of the theory of rational random behavior, respectively.
01 Jul 1979
TL;DR: In this paper, it was shown that the Wilks large sample likelihood ratio statistic behaves as n varies like a diffusion process related to an equilibrium Ornstein-Uhlenbeck process whenever the null hypothesis is true.
Abstract: It is shown that the Wilks large sample likelihood ratio statistic λ n , for testing between composite hypotheses Θ 0 ⊂ Θ 1 on the basis of a sample of size n , behaves as n varies like a diffusion process related to an equilibrium Ornstein-Uhlenbeck process, whenever the null hypothesis is true. This fact is used to construct large sample sequential tests based on λ n , which are the same whatever the underlying distributions. In particular, the underlying distributions need not belong to an exponential family.
TL;DR: In this paper, an estimate of a zero of a complex function, constructed from ordinate information at distinct abscissae, is found from a Maximum Likelihood estimate relative to a normal probability distribution induced by a weak Gaussian distribution on a related Hilbert space.
Abstract: An estimate of a zero of a complex function, constructed from ordinate information at distinct abscissae, is found from a Maximum Likelihood estimate relative to a normal probability distribution induced by a weak Gaussian distribution on a related Hilbert space. In the case of two ordinate observations this leads to an estimator structurally similar to the Secant Rule, and asymptotically approaching that rule in certain limiting situations. A correspondingly modified version of Newton's method is also derived, and regional and asymptotic convergence results proved.
TL;DR: In this paper, it was shown that maximum likelihood estimation of unknown parameters of a linear system with singular observations in general results in the maximization of a likelihood function subject to equality constraints.
Abstract: It is shown that maximum likelihood estimation of unknown parameters of a linear system with singular observations in general results in the maximization of a likelihood function subject to equality constraints.
TL;DR: The likelihood approach is shown to provide a unified framework for treating exact solutions to estimation, prediction, and population-comparison problems in a well defined but non-probabilistic form.
Abstract: This paper reviews the basic ideas of likelihood inference and applies them to some reliability and life testing problems connected with the exponential distribution. Various censoring schemes are considered and the likelihood approach is shown to provide a unified framework for treating exact solutions to estimation, prediction, and population-comparison problems. These solutions are provided in a well defined but non-probabilistic form. The classical s-confidence procedures depend strongly on imaginary exact repetitions of the form of the experiment being analyzed. This is often unrealistic and impractical. The data on hand can be directly analyzed by examining the likelihood function.
TL;DR: This article showed that the likelihood functions for several econometric models are unbounded over certain sequences in parameter space and that the presence of this anomaly becomes less likely as sample size increases.
01 Jan 1979
TL;DR: In this article, the authors examined the asymptotic properties of the maximum likelihood estimator On and of the likelihood ratio statistic An when the model chosen for their construction is incorrect, that is, when no density in the model is a density for the transition probability distribution of the Markov process.
Abstract: Statistical inference for Markov processes is commonly based on the maximum likelihood method of estimation and the likelihood ratio criterion for testing hypotheses. Construction of estimators and test statistics by these methods require that a model be chosen in the form of a family of transition density functions. In this paper, asymptotic properties of the maximum likelihood estimator On and of the likelihood ratio statistic An are examined when the model chosen for their construction is incorrect-that is, when no density in the model is a density for the transition probability distribution of the Markov process. It is shown that if 0, and A, are constructed from a 'regular' incorrect model, then 0, is consistent and asymptotically normally distributed and the asymptotic null distribution of -2 log A, is that of a linear combination of independent chi-squared random variables. These results are applied to propose measures of the performance of the test based on An when the statistic is constructed from an incorrect model.