A study of minimax shrinkage estimators dominating the James-Stein estimator under the balanced loss function

Abstract

One of the most common challenges in multivariate statistical analysis is estimating the mean parameters. A well-known approach of estimating the mean parameters is the maximum likelihood estimator (MLE). However, the MLE becomes inefficient in the case of having large-dimensional parameter space. A popular estimator that tackles this issue is the James-Stein estimator. Therefore, we aim to use the shrinkage method based on the balanced loss function to construct estimators for the mean parameters of the multivariate normal (MVN) distribution that dominates both the MLE and James-Stein estimators. Two classes of shrinkage estimators have been established that generalized the James-Stein estimator. We study their domination and minimaxity properties to the MLE and their performances to the James-Stein estimators. The efficiency of the proposed estimators is explored through simulation studies.

Keywords

• balanced loss function
• james-stein estimator
• multivariate normal distribution
• non-central chi-square distribution
• shrinkage estimators
• 62j07
• 62c20
• 62h10