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