A class of general pretest estimators for the univariate normal mean

Abstract

In this paper, we propose a class of general pretest estimators for the univariate normal mean. The main mathematical idea of the proposed class is the adaptation of randomized tests, where the randomization probability is related to a shrinkage parameter. Consequently, the proposed class includes many existing estimators, such as the pretest, shrinkage, Bayes, and empirical Bayes estimators as special cases. Furthermore, the proposed class can be easily tuned for users by adjusting significance levels and probability function. We derive theoretical properties of the proposed class, such as the expressions for the distribution function, bias, and MSE. Our expressions for the bias and MSE turn out to be simpler than those previously derived for some existing formulas for special cases. We also conduct simulation studies to examine our theoretical results and demonstrate the application of the proposed class through a real dataset.

Keywords:

• Bayes estimator
• Biased estimation
• Mean squared error
• Shrinkage estimation
• Statistical decision theory

Additional information

Funding

Emura T is financially supported by Ministry of Science and Technology, Taiwan (MOST 105-2118-M-008-001-MY2; 107-2118-M-008-003-MY3). Chang YT is financially supported by JSPS KAKENHI Grant Number JP26330047 and JP18K11196.