Estimation of the slope parameter for linear regression model with uncertain prior information

Khan, Shahjahan and Hoque, Zahirul and Saleh, A. K. Md. Ehsanes (2002) Estimation of the slope parameter for linear regression model with uncertain prior information. Journal of Statistical Research, 36. 55- 73. ISSN 0256-422X


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The estimation of the slope parameter of the linear regression model with normal error is considered in this paper when uncertain prior information on the value of the slope is available. Several alternative estimators are defined to incorporate both the sample as well as the non-sample information in the estimation process. Some 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. Both analytical and graphical methods are explored. None of the estimators is found to be uniformly superior over the others. However, if the non-sample information regarding the value of the slope is close to its true value, the shrinkage estimator over performs the rest of the estimators.

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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Depositing User: Professor Shahjahan Khan
Faculty / Department / School: Historic - Faculty of Sciences - Department of Maths and Computing
Date Deposited: 11 Oct 2007 00:37
Last Modified: 02 Jul 2013 22:36
Uncontrolled Keywords: Uncertain non-sample prior information; maximum likelihood, restricted, preliminary test and shrinkage estimators; bias, mean square error and relative efficiency; normal, Student-t, non-central chi-square and F distributions; and incomplete beta ratio.
Fields of Research (FOR2008): 01 Mathematical Sciences > 0104 Statistics > 010405 Statistical Theory

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