On the comparison of the pre-test and shrinkage estimators for the univariate normal mean
Article
Article Title | On the comparison of the pre-test and shrinkage estimators for the univariate normal mean |
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ERA Journal ID | 857 |
Article Category | Article |
Authors | Khan, Shahjahan (Author) and Saleh, A. K. Md. E. (Author) |
Journal Title | Statistical Papers |
Journal Citation | 42 (4), pp. 451-473 |
Number of Pages | 23 |
Year | 2001 |
Place of Publication | Germany |
ISSN | 0932-5026 |
1613-9798 | |
Web Address (URL) | http://www.springerlink.com/content/mbqc7a26qm6cf41c/fulltext.pdf |
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. |
Keywords | uncertain non-sample prior information; maximum likelihood;restricted; preliminary test and shrinkage estimators; bias; mean square error; relative efficiency; normal; student; non-central chi-square and F distributions; incomplete beta ratio |
ANZSRC Field of Research 2020 | 490599. Statistics not elsewhere classified |
490509. Statistical theory | |
Public Notes | Accepted version deposited in accordance with the copyright policy of the publisher. Copyright 2001 Springer. This is the author's version of the work. It is posted here with permission of the publisher for your personal use. No further distribution is permitted. The original publication is available at: http://www.springerlink.com |
Byline Affiliations | Department of Mathematics and Computing |
Carleton University, Canada |
https://research.usq.edu.au/item/9xvx7/on-the-comparison-of-the-pre-test-and-shrinkage-estimators-for-the-univariate-normal-mean
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