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 language | English |
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Pages (from-to) | 742-752 |
Number of pages | 11 |
Journal | Journal of Multivariate Analysis |
Volume | 100 |
Issue number | 4 |
DOIs | |
Publication status | Published - Apr 2009 |
Externally published | Yes |
Keywords
- 62C15
- 62H12
- Decision theoretic estimation
- Estimation of the precision matrix
- Multivariate Kotz type model
- Quadratic loss
- primary
- secondary
ASJC Scopus subject areas
- Statistics and Probability
- Numerical Analysis
- Statistics, Probability and Uncertainty