Estimation of the precision matrix of multivariate Kotz type model

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 α 0 A − 1 , where A denotes the sample sum of product matrix, is dominated by a better constant multiple of A − 1 , denoted by α 0 ⋆ A − 1 . Secondly, a new class of shrinkage estimators of Σ − 1 is proposed. Moreover, the risk functions of α 0 A − 1 , α 0 ⋆ A − 1 and the proposed estimators are explicitly derived. It is shown that the proposed estimator dominates α 0 ⋆ 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.