Title: A class of general pretest estimators for the normal means
Authors: Jia-Han Shih - National Central University (Taiwan) [presenting]
Yoshihiko Konno - Japan Womens University (Japan)
Genso-Y. T. Watanabe-Chang - Mejiro University (Japan)
Takeshi Emura - Kurume University (Japan)
Abstract: For estimating a large number of mean parameters, univariate analyses remain the most popular approach in real applications due to its simplicity. Such analyses typically perform some preliminary tests (e.g. t-tests) to reduce the number of variables and impose some sparsity assumptions to shrink the estimates. To handle these tasks simultaneously, we propose a class of general pretest estimators that include many existing pretest, shrinkage, Bayes, and empirical Bayes estimators as special cases. We adopt the idea of randomized tests to construct a class of general pretest estimators, where the randomization probability is related to a shrinkage parameter. Theoretical properties of the proposed pretest estimator such as the exact distribution, bias, and mean squared error are derived. Our new expressions for the bias and mean squared error are simpler and more straightforward than the existing ones. We illustrate the use of the proposed estimator through the analysis of high-dimensional gene-expressions.