Abstract
The problem of estimating the regression coefficients in the usual regression model is considered when it is a priori suspected that the coefficients may be restricted to a subspace. Four estimators, namely, the unrestricted least squares estimator (ULSE), restricted least squares estimator (RLSE), preliminary test estimator (PTE) and shrinkage estimator (SE) are given. Further, we show that proposed SE is the empirical Bayes estimator (EBE) under certain prior distribution. The RLSE has the smallest risk when the hypothesis that the regression coefficients satisfy the restriction holds. However, the risk of RLSE is unbounded when the parameter moves away from the subspace of the restriction. The SE has the smallest risk in most cases except when the parameter is in near the null hypothesis; in such case the PTE is better.
