Shrinkage estimators of intercept parameters of two simple regression models with suspected equal slopes

Khan, Shahjahan (2008) Shrinkage estimators of intercept parameters of two simple regression models with suspected equal slopes. Communications in Statistics: Theory and Methods, 37 (2). pp. 247-260. ISSN 0361-0926

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Abstract

Estimators of the intercept parameter of a simple linear regression model involves the slope estimator. In this article, we consider the estimation of the intercept parameters of two linear regression models with normal errors, when it is a priori suspected that the two regression lines are parallel, but in doubt. We also introduce a coefficient of distrust as a measure of degree of lack of trust on the uncertain prior information regarding the equality of two slopes. Three different estimators of the intercept parameters are defined by using the sample data, the non sample uncertain prior information, an appropriate test statistic, and the coefficient of distrust. The relative performances of the unrestricted, shrinkage restricted and shrinkage preliminary test estimators are investigated based on the analyses of the bias and risk functions under quadratic loss. If the prior information is precise and the coefficient of distrust is small, the shrinkage preliminary test estimator overperforms the other estimators. An example based on a medical study is used to illustrate the method.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Author version deposited in accordance with the copyright policy of publisher.
Depositing User: Professor Shahjahan Khan
Faculty / Department / School: Historic - Faculty of Sciences - Department of Maths and Computing
Date Deposited: 08 Jan 2008 23:46
Last Modified: 02 Jul 2013 22:56
Uncontrolled Keywords: central and non central F-distribution; coefficient of distrust; non sample uncertain prior information; parallel regression lines; quadratic bias; shrinkage restricted and preliminary test estimators.
Fields of Research (FOR2008): 01 Mathematical Sciences > 0104 Statistics > 010406 Stochastic Analysis and Modelling
01 Mathematical Sciences > 0104 Statistics > 010405 Statistical Theory
01 Mathematical Sciences > 0102 Applied Mathematics > 010202 Biological Mathematics
Socio-Economic Objective (SEO2008): E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
Identification Number or DOI: doi: 10.1080/03610920701648961
URI: http://eprints.usq.edu.au/id/eprint/3715

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