Asymptotic shrinkage estimation: The regression case

In this paper, we first outline some recent developments in the area of pretest and shrinkage estimation. We discuss various large sample estimation techniques in a regression model when the error terms are not necessarily normally distributed. The commonly asked question whether to combine sample data and nonsample information (NSI) or uncertain prior information (UPI) will be systematically addressed. We propose estimators on the basis of preliminary tests or significance and James-Stein rule. The properties oi these estimators are studied in the problem of estimating regression coefficients in the multiple regression model when it is apriori suspected that the coefficients may be restricted to a subspace.