SHRINKAGE PRE-TEST ESTIMATOR OF THE UNIVARIATE NORMAL MEAN

Yüksel G., Billor N., Ünal D.

PAKISTAN JOURNAL OF STATISTICS, vol.26, no.3, pp.461-477, 2010 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 26 Issue: 3
  • Publication Date: 2010
  • Journal Name: PAKISTAN JOURNAL OF STATISTICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.461-477
  • Çukurova University Affiliated: Yes

Abstract

Estimation of the mean of a univariate normal population with, unknown variance is a well-known problem in the presence of an uncertain prior information. In this study, we propose a new estimator, shrinkage pre-test estimator, which is a combination of pre-test and shrinkage estimators. The mean squared error (MSE) for the shrinkage pre-test estimator is also derived and theoretical comparisons based on MSE criterion of this new estimator with the restricted, the pre-test, and the shrinkage estimators are given. We show that the shrinkage pre-test estimator performs better than the other existing estimators. In addition, the performance of this newly proposed estimator is being assessed by conducting a simulation study.