Estimation of the precision matrix of multivariate Kotz type model

Abstract

In this paper, the problem of estimating the precision matrix of a multivariate Kotz type model is considered. First, using the quadratic loss function, we prove that the unbiased estimator α0 A- 1, where A denotes the sample sum of product matrix, is dominated by a better constant multiple of A- 1, denoted by α0{star operator} A- 1. Secondly, a new class of shrinkage estimators of Σ- 1 is proposed. Moreover, the risk functions of α0 A- 1, α0{star operator} A- 1 and the proposed estimators are explicitly derived. It is shown that the proposed estimator dominates α0{star operator} A- 1, under the quadratic loss function. A simulation study is carried out which confirms these results. Improved estimator of tr (Σ- 1) is also obtained.