r-k CLASS ESTIMATION IN REGRESSION MODEL WITH CONCOMITANT VARIABLES

MASAYUKI JIMICHI^{1} AND NOBUO INAGAKI^{2}

1School of Business Administration, Kwansei Gakuin University, 1-155, Uegaharaichiban-cho, Nishinomiya, Hyogo 662, Japan

2Department of Mathematical Science, Faculty of Engineering Science, Osaka University, Machikaneyama-cho, Toyonaka, Osaka 560, Japan

(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.