On shrinkage least squares estimation in a parallelism problem

Abstract

In a multi-sample simple regression model, generally, homogeneity of the regression slopes leads to improved estimation of the intercepts. Analogous to the preliminary test estimators, (smooth) shrinkage least squares estimators of Intercepts based on the James-Stein rule on regression slopes are considered. Relative pictures on the (asymptotic) risk of the classical, preliminary test and the shrinkage least squares estimators are also presented. None of the preliminary test and shrinkage least squares estimators may dominate over the other, though each of them fares well relative to the other estimators.

Keywords:

• Asymptotic distribution
• asymptotic distributional risk
• homogeneity of regression slopes
• intercepts
• James-Stein rule
• least squares estimation
• preliminary test estimation
• shrinkage estimation