Asymptotically optimal shrinkage estimates for non-normal data

作者：Withers Christopher S; Nadarajah Saralees^*

来源：Journal of Statistical Computation and Simulation, 2011, 81(12): 2021-2037.

DOI：10.1080/00949655.2010.515592

• multiple shrinkage estimates
• Stein estimate

Motivated by several practical issues, we consider the problem of estimating the mean of a p-variate population (not necessarily normal) with unknown finite covariance. A quadratic loss function is used. We give a number of estimators (for the mean) with their loss functions admitting expansions to the order of p(-1/2) as p -> infinity. These estimators contain Stein's [Inadmissibility of the usual estimator for the mean of a multivariate normal population, in Proceedings of the Third Berkeley Symposium in Mathematical Statistics and Probability, Vol. 1, J. Neyman, ed., University of California Press, Berkeley, 1956, pp. 197-206] estimate as a particular case and also contain 'multiple shrinkage' estimates improving on Stein's estimate. Finally, we perform a simulation study to compare the different estimates.

• 出版日期2011