Statistical Inference for Models with Multivariate t-Distributed Errors

CHAPTER 1

INTRODUCTION

Outline

1.1 Objective of the Book

1.2 Models under Consideration

1.3 Organization of the Book

1.4 Problems

1.1 Objective of the Book

The classical theory of statistical analysis is primarily based on the assumption that the errors of various models are normally distributed. The normal distribution is also the basis of the (i) chi-square, (ii) Student’s t-, and (iii) F-distributions. Fisher (1956) pointed out that slight differences in the specification of the distribution of the model errors may play havoc on the resulting inferences. To examine the effects on inference, Fisher (1960) analyzed Darwin’s data under normal theory and later under a symmetric non-normal distribution. Many researchers have since investigated the influence on inference of distributional assumptions differing from normality. Further, it has been observed that most economic and business data, e.g., stock return data, exhibit long-tailed distributions. Accordingly, Fraser and Fick (1975) analyzed Darwin’s data and Baltberg and Gonedes (1974) analyzed stock returns using a family of Student’s t-distribution to record the effect of distributional assumptions compared to the normal theory analysis. Soon after, Zellner (1976) considered analyzing stock return data by a simple regression model, assuming the error distribution to have a multivariate t-distribution. He revealed the fact that dependent but uncorrelated responses can be analyzed by multivariate t-distribution. He discussed ...