Statistical Inference for Models with Multivariate t-Distributed Errors

PREFACE

In problems of statistical inference, it is customary to use normal distribution as the basis of statistical analysis. Many results related to univariate analysis can be extended to multivariate analysis using multidimensional normal distribution. Fisher (1956) pointed out, from his experience with Darwin’s data analysis, that a slight change in the specification of the distribution may play havoc on the resulting inferences. To overcome this problem, statisticians tried to broaden the scope of the distributions and achieve reasonable inferential conclusions. Zellner (1976) introduced the idea of using Student’s t-distribution, which can accommodate the heavier tailed distributions in a reasonable way and produce robust inference procedures for applications. Most of the research with Student’s t-distribution, so far, is focused on the agreement of the results with that of the normal theory. For example, the maximum likelihood estimator of the location parameter agrees with the mean-vector of a normal distribution. Similarly, the likelihood ratio test under the Student’s t-distribution has same distribution as the normal distribution under the null hypothesis. This book is an attempt to fill the gap in statistical inference on linear models based on the multivariate t-errors.

This book consists of 12 chapters. Chapter 1 summarizes the results of various models under normal theory with a brief review of the literature. Chapter 2 contains the basic properties of various known ...