Comparisons of the <Emphasis Type="Italic">r</Emphasis> − <Emphasis Type="Italic">k</Emphasis> class estimator to the ordinary least squares estimator under the Pitman’s closeness criterion |
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Authors: | M Revan Özkale Selahattin Kaçıranlar |
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Affiliation: | 1.Faculty Science and Letters, Department of Statistics,?ukurova University,Adana,Turkey |
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Abstract: | In the presence of multicollinearity, the r − k class estimator is proposed as an alternative to the ordinary least squares (OLS) estimator which is a general estimator
including the ordinary ridge regression (ORR), the principal components regression (PCR) and the OLS estimators. Comparison
of competing estimators of a parameter in the sense of mean square error (MSE) criterion is of central interest. An alternative
criterion to the MSE criterion is the Pitman’s (1937) closeness (PC) criterion. In this paper, we compare the r − k class estimator to the OLS estimator in terms of PC criterion so that we can get the comparison of the ORR estimator to the
OLS estimator under the PC criterion which was done by Mason et al. (1990) and also the comparison of the PCR estimator to
the OLS estimator by means of the PC criterion which was done by Lin and Wei (2002). |
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Keywords: | Multicollinearity Pitman closeness criterion r − k class estimator Ordinary ridge regression estimator Principal components regression estimator |
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