Statistical Inference for Models with Multivariate t-Distributed Errors

CHAPTER 5

ANOVA

Outline

5.1 Model Specification

5.2 Proposed Estimators and Testing

5.3 Bias, MSE, and Risk Expressions

5.4 Risk Analysis

5.5 Problems

In this chapter, we will discuss the ANOVA model in detail, beginning with the estimation of the model parameters and test of hypothesis. In addition, we shall provide some improved estimators of the ANOVA parameters with their dominance properties. Also included are various estimators of the scale parameter in the model along with their comparisons.

5.1 Model Specification

The analysis of variance (ANOVA) is a set of statistical techniques for studying the variability from different sources and comparing them to understand the relative importance of each the sources. It is also used to make inferences about the populations through the test of significance, including the very important comparison of two or more means of the population concerned. ANOVA is one of the most important models among many models belonging to the class of general linear models. This model may be written compactly as

(5.1.1)

where

(5.1.2)

in which y_ij is the value of measurement,

(5.1.3)

is the block diagonal vectors, where 1_nα = (1, …, 1)′ is a n_α-tuple of 1’s, ...