Estimation of the precision matrix of multivariate Kotz type model

Amadou Sarr, Arjun K. Gupta

Research output: Contribution to journalArticle

9 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)742-752
Number of pages11
JournalJournal of Multivariate Analysis
Volume100
Issue number4
DOIs
Publication statusPublished - Apr 2009

Keywords

  • 62C15
  • 62H12
  • Decision theoretic estimation
  • Estimation of the precision matrix
  • Multivariate Kotz type model
  • primary
  • Quadratic loss
  • secondary

ASJC Scopus subject areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

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