Showing papers by "T. W. Anderson published in 1982"
TL;DR: In this article, the authors present a statistical analysis of time series regression models for longitudinal data with and without lagged dependent variables under a variety of assumptions about the initial conditions of the processes being analyzed.
2,774 citations
TL;DR: In this paper, the distributions of the Limited Information Maximum Likelihood estimator for the coefficient of one endogenous variable are evaluated numerically and compared with the Two-Stage Least Squares estimator.
Abstract: The distributions of the Limited Information Maximum Likelihood estimator for the coefficient of one endogenous variable are evaluated numerically. Tables are given for enough values of the parameters to cover all cases of interests. Comparisons are made with the Two-Stage Least Squares estimator.
127 citations
TL;DR: For a class of multivariate elliptically contoured distributions, the maximum likelihood estimators of the mean vector and covariance matrix were found under certain conditions in this article, and the likelihood-ratio criteria were obtained for the same form as in the normal case.
Abstract: For a class of multivariate elliptically contoured distributions the maximum-likelihood estimators of the mean vector and covariance matrix are found under certain conditions. Likelihood-ratio criteria are obtained for a class of null hypotheses. These have the same form as in the normal case.
105 citations
01 May 1982
TL;DR: In this paper, a special class of multivariate elliptically contoured distributions is studied in detail, which generalize the elliptically-constructed distribution to the case of a matrix.
Abstract: : In this paper, the multivariate elliptically contoured distributions which generalize the elliptically contoured distribution to the case of a matrix are defined and a special class of multivariate elliptically contoured distributions is studied in detail. For this class we obtain the distributions of the following statistics: correlation coefficients, multiple correlation coefficients, Hotelling's T2, sample covariance matrix, generalized variance, characteristic roots of the covariance matrix, quadratic forms, etc. Some multivariate statistical applications are discussed. (Author)
48 citations
35 citations
TL;DR: In this paper, a new proof of admissibility of tests in MANOVA is given using Stein's theorem, which is proved directly by means of majorization rather than by the supporting hyperplane approach.
7 citations
01 Jan 1982
TL;DR: In this paper, the exact density and distribution of the maximum likelihood estimator of the slope of a linear functional relationship are obtained, and their accuracies are discussed, and an expansion of the distribution is obtained to a term of one higher order than Anderson (1974).
Abstract: SUMMARY When the errors are normally independently distributed with equal variance, the maximum likelihood estimator of the slope of a linear functional relationship is the slope of the line minimizing the sum of squared deviations orthogonal to the line. The exact density and distribution of this estimator are obtained. Approximate distributions are obtained, and their accuracies are discussed. IN the model of a linear functional relationship between two variables with independent normal errors of observation with equal variances the maximum likelihood (ML) estimator of the slope is the slope of the line fitted to minimize the sum of squared distances of the observed points from the line. In this paper the exact density function of the ML estimator is given; the cumulative distribution function is also given in a form suitable for computation, a convergent infinite series of incomplete beta functions. In addition an expansion of the distribution is obtained to a term of one higher order than Anderson (1974). Another asymptotic expansion is based on the doubly noncentral F-distribution. The latter will be shown accurate enough to be regarded as virtually exact if the noncentrality parameter is moderately large; hence it can be used to evaluate numerically the exact cumulative distribution function of the ML estimator.
2 citations