Estimation of the precision matrix of multivariate Kotz type model

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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 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.

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Sarr, A., & Gupta, A. K. (2009). Estimation of the precision matrix of multivariate Kotz type model. Journal of Multivariate Analysis, 100(4), 742–752. https://doi.org/10.1016/j.jmva.2008.08.001

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