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 α0A−1, where A denotes the sample sum of product matrix, is dominated by a better constant multiple of A−1, denoted by α0⋆A−1. Secondly, a new class of shrinkage estimators of Σ−1 is proposed. Moreover, the risk functions of α0A−1, α0⋆A−1 and the proposed estimators are explicitly derived. It is shown that the proposed estimator dominates α0⋆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.