Estimation of the precision matrix of multivariate Kotz type model

  • Authors:

  • Amadou Sarr;Arjun K. Gupta

  • Affiliations:

  • Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43403, USA;Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43403, USA

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2009

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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 @a"0A^-^1, where A denotes the sample sum of product matrix, is dominated by a better constant multiple of A^-^1, denoted by @a"0^@?A^-^1. Secondly, a new class of shrinkage estimators of @S^-^1 is proposed. Moreover, the risk functions of @a"0A^-^1, @a"0^@?A^-^1 and the proposed estimators are explicitly derived. It is shown that the proposed estimator dominates @a"0^@?A^-^1, under the quadratic loss function. A simulation study is carried out which confirms these results. Improved estimator of tr(@S^-^1) is also obtained.