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Statistical Inference for Models with Multivariate t-Distributed Errors by A. K. Md. Ehsanes Saleh, Mohammad Arashi, S M M Tabatabaey

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CHAPTER 4

SIMPLE REGRESSION MODEL

Outline

4.1 Introduction

4.2 Estimation and Testing of η

4.3 Properties of Intercept Parameter

4.4 Comparison

4.5 Numerical Illustration

4.6 Problems

In this chapter, we discuss some of the basic results from a simple regression model under the assumption that the error-vector is distributed according to the multivariate t-distribution. For normal errors see Saleh (2006) and for t-errors see Khan and Saleh (1997, 2008).

4.1 Introduction

Consider a simple linear model

(4.1.1) equation

where Y = (Y1, Y2, …, Yn)′ is the response vector and x = (x1, x2, …, xn)′ is a fixed vector of known constants, while ε = (ε1, ε2, …, εn)′ is the error vector distributed according to the low belonging to the class of multivariate t-distributions, say, M(n)t (0, σ2Vn, γo).

As in Chapter 3, the covariance matrix is formulated as

(4.1.2) equation

4.2 Estimation and Testing of η

In this section, we consider LSE of η and test of hypothesis, H0 : η = ηo vs HA : ηηo.

4.2.1 Estimation of η

For the LSE of η, we minimize

equation

to obtain the LSE of η as

(4.2.1) equation

where

(4.2.2)

with K1 = 1′V−1n1, K

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