Double shrinkage estimation of common coefficients in two regression equations with heteroscedasticity

The problem of estimating the common regression coefficients is addressed i n this paper for two regression equations with possibly different error var iances. The feasible generalized least squares (FGLS) estimators have been believed to be admissible within the class of unbiased estimators. It is, n evertheless, established that the FGLS estimators are inadmissible in light of minimizing the covariance matrices if the dimension of the common regre ssion coefficients is greater than or equal to three. Double shrinkage unbi ased estimators are inadmissible in light of minimizing the covariance matr ices if the dimension of the common regression coefficients is greater than or equal to three. Double shrinkage unbiased estimators are proposed as po ssible candidates of improved procedures. (C) 1998 Academic Press.