(Received August 8, 1994; revised April 25, 1995)
Abstract. We treat with the r-k class estimation in a regression model, which includes the ordinary least squares estimator, the ordinary ridge regression estimator and the principal component regression estimator as special cases of the r-k class estimator. Many papers compared total mean square error of these estimators. Sarkar (1989, Ann. Inst. Statist. Math., 41, 717-724) asserts that the results of this comparison are still valid in a misspecified linear model. We point out some confusions of Sarkar and show additional conditions under which his assertion holds.
Key words and phrases: Concomitant variables, multicollinearity, ordinary least squares estimator, ordinary ridge regression estimator, principal component regression estimator, r-k class estimator.