Title: Improved shrinkage estimation of squared multiple correlation coefficient and squared cross-validity coefficient
Authors: Shieh, Gwowen
Department of Management Science
Keywords: bias;maximum likelihood estimator;mean square error;multiple linear regression;shrinkage estimator
Issue Date: 1-Apr-2008
Abstract: The sample squared multiple correlation coefficient is widely used for describing the usefulness of a multiple linear regression model in many areas of science. In this article, the author considers the problem of estimating the squared multiple correlation coefficient and the squared cross-validity coefficient under the assumption that the response and predictor variables have a joint multinormal distribution. Detailed numerical investigations are conducted to assess the exact bias and mean square error of the proposed modifications of established estimators. Notably, the positive-part Pratt estimator and the synthesis of Browne and positive-part Pratt estimators are recommended in the estimation of squared multiple correlation coefficient and squared cross-validity coefficient, respectively, for their overall advantages of incurring the least amount of statistical discrepancy and computational requirement.
URI: http://dx.doi.org/10.1177/1094428106292901
ISSN: 1094-4281
DOI: 10.1177/1094428106292901
Volume: 11
Issue: 2
Begin Page: 387
End Page: 407
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