Showing papers by "T. W. Anderson published in 1994"

Inference in linear models

Abstract: matrix of unobservable random variables. The elements of X may be observable or alternatively unobservable (that is, latent); they may be nonstochastic or stochastic. The model includes regression, linear functional and structural relations, multivariate analysis of variance, factor analysis, and some simultaneous equations models. This paper considers the relationships between various models and presents methods of estimating the parameters under various conditions. Testing hypotheses about the rank of XB! (the dimensionality of the latent variables when X is not observed) are also treated. 1. A Linear Model. In this paper we consider a general linear model in multivariate analysis that includes regression models, multivariate analysis of variance (MANOVA) models, and factor analysis models. Some of these models go by names of linear functional relationships, linear structural relationships, and canonical correlations. An attempt will be made to use a unified approach to these models. Suppose we observe the ? x 1 vectors y\, ? ? ? , y^. A linear model is given

The Modified Cramer-von Mises Goodness-of-Fit Criterion for Time Series

Abstract: : In this paper we consider somewhat analogous quadratic forms in normal variables when the dimensionality is infinite. Then the quadratic forms are distributed infinite weighted SUMS Of X2 -variables. These come about as goodness-of-fit criteria for a hypothesis that a cumulative distribution function is a specified one or that two cdf's are the same. Such criteria also arise for goodness-of-fit tests for standardized spectral distributions. As examples, we give tables of the distribution of the criterion for testing the hypothesis that a stationary stochastic process is a given moving average process order 1 and for testing the hypothesis that it is a specified autoregressive process order 1. Two methods are described for calculating the distribution. Either method is appropriate for calculating the distribution of the criterion for testing the hypothesis that a process is a stationary process whose standardized spectral density of distribution is a specified one. Goodness of fit, Time series, Mahalanobis distance, Stationary stochastic process, Spectral distributions.