Double Shrinkage Estimation of Common Coefficients in Two Regression Equations with Heteroscedasticity

Abstract

The problem of estimating the common regression coefficients is addressed in this paper for two regression equations with possibly different error variances. The feasible generalized least squares (FGLS) estimators have been believed to be admissible within the class of unbiased estimators. It is, nevertheless, established that the FGLS estimators are inadmissible in light of minimizing the covariance matrices if the dimension of the common regression coefficients is greater than or equal to three. Double shrinkage unbiased estimators are proposed as possible candidates of improved procedures. Academic PressAMS 1991 subject classifications: primary 62C15; secondary 62F11, 62H12, 62J05.

Heteroscedasticity diagnostics in two-phase linear regression models

“…It is worth noting that the condition that both of X 1 and X 2 have rank p may be reduced to Rank(X 1 + X 2 ) = p. With respect to two-phase regression model, the basic problem is to estimate the common regression coefficient vector β when the σ k s(k = 1, 2) are unknown. Swamy [11] and Kubokawa [12] obtained some results on this aspect. However, their work was all based on the standard assumption that the random errors of both phases have constant variances, that is, Q k is the identity matrices, k = 1, 2.…”