TY - JOUR
T1 - Estimation of the precision matrix of multivariate Kotz type model
AU - Sarr, Amadou
AU - Gupta, Arjun K.
PY - 2009/4
Y1 - 2009/4
N2 - 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.
AB - 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.
KW - 62C15
KW - 62H12
KW - Decision theoretic estimation
KW - Estimation of the precision matrix
KW - Multivariate Kotz type model
KW - Quadratic loss
KW - primary
KW - secondary
UR - http://www.scopus.com/inward/record.url?scp=58349100663&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=58349100663&partnerID=8YFLogxK
U2 - 10.1016/j.jmva.2008.08.001
DO - 10.1016/j.jmva.2008.08.001
M3 - Article
AN - SCOPUS:58349100663
SN - 0047-259X
VL - 100
SP - 742
EP - 752
JO - Journal of Multivariate Analysis
JF - Journal of Multivariate Analysis
IS - 4
ER -