Estimation of a Conditional Mean in a Linear Regression Model after a Preliminary Test on Regression Coefficient

✍ Scribed by Dinesh S. Bhoj; Mohammad Ahsanullah

• Publisher: John Wiley and Sons
• Year: 1994
• Tongue: English
• Weight: 449 KB
• Volume: 36
• Category: Article
• ISSN: 0323-3847
• DOI: 10.1002/bimj.4710360206

✦ Synopsis

Abstract

Consider the two linear regression models of Y~ij~ on X~ij~, namely Y~ij~ = β~io~ + β~ij~, X~ij~ + E~ij~ = 1, 2,…, n~i~, i = 1, 2, where E~ij~ are assumed to be normally distributed with zero mean and common unknown variance σ^2^. The problem of estimating the conditional mean of Y~1~ for a given value of X~1~ is considered when it is a priori suspected that β~10~ = β~20~ and β~11~ = β~21~. The preliminary test estimator is proposed. The exact expressions for the bias and the mean square error of the estimator are derived. The relative efficiency of the new estimator to the usual least square estimator based on the first regression alone is computed and is used to determine the appropriate value of the significance level of the preliminary test β~10~ = β~20~ and β~11~ = β~21~.