TY  - JOUR
AU  - Hamdaoui, Abdenour 
AU  - Mezouar, Nadia 
PY  - 2017
TI  - Risks Ratios of Shrinkage Estimators for the Multivariate Normal Mean
JF  - Journal of Mathematics and Statistics
VL  - 13
IS  - 2
DO  - 10.3844/jmssp.2017.77.87
UR  - https://thescipub.com/abstract/jmssp.2017.77.87
AB  - We study the estimation of the mean θ of a multivariate Gaussian random variable X∼Np(θ,σ2Ip) in ℜp, σ2 is unknown and estimated by the chi-square variable S2∼σ2χn2. In this work we are interested in studying bounds and limits of risk ratios of shrinkage estimators to the maximum likelihood estimator X, when n and p tend to infinity. We recall that the risk ratios of shrinkage estimators to the maximum likelihood estimator has a lower bound Bm, when n and p tend to infinity. We show that if the shrinkage function ψ(S2,||X2||) satisfies some conditions, the risk ratios of shrinkage estimators (1-ψ(S2,||X2||)S2/||X2||)X, which did not inevitably minimax, to attain the limiting lower bound Bm which is strictly lower than 1.