On the comparison of the pre-test and shrinkage estimators for the univariate normal mean |
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Authors: | Shahjahan Khan A K Md E Saleh |
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Institution: | (1) Department of Mathematics and Computing, University of Southern Queensland, Toowoomba, Queensland, Australia, AU;(2) School of Mathematics and Statistics, Carleton University, Ottawa, Canada, CA |
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Abstract: | The estimation of the mean of an univariate normal population with unknown variance is considered when uncertain non-sample
prior information is available. Alternative estimators are defined to incorporate both the sample as well as the non-sample
information in the estimation process. Some of the important statistical properties of the restricted, preliminary test, and
shrinkage estimators are investigated. The performances of the estimators are compared based on the criteria of unbiasedness
and mean square error in order to search for a ‘best’ estimator. Both analytical and graphical methods are explored. There
is no superior estimator that uniformly dominates the others. However, if the non-sample information regarding the value of
the mean is close to its true value, the shrinkage estimator over performs the rest of the estimators.
Received: June 19, 1999; revised version: March 23, 2000 |
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Keywords: | AMS 1990 Subject Classification: Primary 62F30 Secondary 62H12 and 62F10 |
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