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*r-k* CLASS ESTIMATION IN REGRESSION MODEL

WITH CONCOMITANT VARIABLES

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

^{1} *School of Business Administration, Kwansei Gakuin
University,*

1-155, Uegaharaichiban-cho, Nishinomiya, Hyogo 662, Japan

^{2} *Department 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.

**Source**
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