Asymptotic properties of risks ratios of shrinkage estimators

Hamdaoui Abdenour, Benmansour Djamel
2014 Hacettepe Journal of Mathematics and Statistics  
We study the estimation of the mean of a multivariate normal distribution N p , 2 I p in p , 2 is unknown and estimated by the chi-square variable S 2 2 n 2 . In this work we are interested in studying bounds and limits of risk ratios of shrinkage estimators to the maximum likelihood estimator, when n and p tend to infinity provided that lim p 2 p 2 c. The risk ratio for this class of estimators has a lower bound B m c 1 c , when n and p tend to infinity provided that lim p 2 p 2 c. We give
more » ... p 2 c. We give simple conditions for shrinkage minimax estimators, to attain the limiting lower bound B m . We also show that the risk ratio of James-Stein estimator and those that dominate it, attain this lower bound B m (in particularly its positive-part version). We graph the corresponding risk ratios for estimators of James-Stein JS , its positive part JS , that of a minimax estimator, and an estimator dominating the James-Stein estimator in the sense of the quadratic risk ( polynomial estimators proposed by Tze Fen Li and Hou Wen Kuo [13]) for some values of n and p.
doi:10.15672/hjms.2014377624 fatcat:jnj4mzzkmjdv7bx2fyqqd7y5my