A restricted $$r{-}k$$ r - k class estimator in the mixed regression model with autocorrelated disturbances

Abstract

In this paper, a new estimator is proposed by combining basically the ordinary ridge regression estimator and the principal component regression estimator for a regression model which has multicollinearity and which satisfies some a priori stochastic linear restrictions. The performance of the proposed \(r{-}k\) class estimator in this mixed regression model is compared with those of the mixed regression estimator, ridge regression estimator and the stochastic restricted ridge regression estimator in terms of the mean squared error matrix criterion. Tests for verifying the conditions of dominance of the proposed estimator over the others are also proposed. Furthermore, a Monte Carlo study and a numerical illustration are carried out to empirically study the performance of the estimators by the mean squared error values, and then to perform tests to verify if the conditions for superiority of the proposed estimator over the others hold.