General Classes of Shrinkage Estimators for the Multivariate Normal Mean with Unknown Variance: Minimaxity and Limit of Risks Ratios
ABDELKADER BENKHALED, Abdenour Hamdaoui
Abstract
In this paper, we consider two forms of shrinkage estimators of the mean of a multivariate normal distribution X N p , 2 I p in R p where 2 is unknown and estimated by the statistic S 2 (S 2 2 2 n ). Estimators that shrink the components of the usual estimator X to zero and estimators of Lindley-type, that shrink the components of the usual estimator to the random variable X. Our aim is to improve under appropriate condition the results related to risks ratios of shrinkage estimators, when n and p tend to infinity and to ameliorate the results of minimaxity obtained previously of estimators cited above, when the dimension p is finite. Some numerical results are also provided.
Topics & Concepts
EstimatorMathematicsDimension (graph theory)ShrinkageStatisticsMultivariate statisticsStatisticLimit (mathematics)Shrinkage estimatorVariance (accounting)Multivariate normal distributionApplied mathematicsCombinatoricsMinimum-variance unbiased estimatorBias of an estimatorMathematical analysisBusinessAccountingStatistical Distribution Estimation and ApplicationsStatistical Methods and InferenceProbability and Risk Models