Improved shrinkage estimation of squared multiple correlation coefficient and squared cross-validity coefficient

Gwowen Shieh*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

26 Scopus citations

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.

Original languageEnglish
Pages (from-to)387-407
Number of pages21
JournalOrganizational Research Methods
Volume11
Issue number2
DOIs
StatePublished - 1 Apr 2008

Keywords

  • Bias
  • Maximum likelihood estimator
  • Mean square error
  • Multiple linear regression
  • Shrinkage estimator

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