Estimation of the precision matrix of multivariate Kotz type model

Abstract

a b s t r a c tIn 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 −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( −1 ) is also obtained.Published by Elsevier Inc.

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