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r-k Class estimation in regression model with concomitant variables
Authors:Masayuki Jimichi  Nobuo Inagaki
Institution:(1) School of Business Administration, Kwansei Gakuin University, 1-155, Uegaharaichiban-cho, 662 Nishinomiya, Hyogo, Japan;(2) Department of Mathematical Science, Faculty of Engineering Science, Osaka University, Machikaneyama-cho, 560 Toyonaka, Osaka, Japan
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.
Keywords:Concomitant variables  multicollinearity  ordinary least squares estimator  ordinary ridge regression estimator  principal component regression estimator  r-k class estimator
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