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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 3

LOCATION MODEL

Outline

3.1 Model Specification

3.2 Unbiased Estimates of θ and σ2 and Test of Hypothesis

3.3 Estimators

3.4 Bias and MSE Expressions of the Location Estimators

3.5 Various Estimates of Variance

3.6 Problems

In this chapter, we discuss some basic results on the location model under the assumption that the error-vector is distributed according to the multivariate t-distribution.

3.1 Model Specification

Consider the location model with the response vector Y = (Y1, ···, Yn)′ such that it satisfies the relation

(3.1.1) equation

where 1n = (1, ···, 1)′ is an n-tuple of 1’s, and the error vector ε follows the multivariate M(n)t(0, σ2Vn γo) with pdf

equation

where σ > 0, Vn is a positive definite matrix of rank n and γo > 2.

The mean of ε is the zero-vector and the covariance-matrix of ε is

(3.1.2) equation

The plan of this chapter is as follows. In sections 2 and 3, unbiased estimators of θ and σ2ε are proposed along with the test statistic for testing the hypothesis H0 : θ = θ0. In addition, we propose some improved estimates of location parameter. Section 4 contains some important theorems for the bias and MSE expressions of the proposed estimators of θ and their mathematical characteristics. ...

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