TY - JOUR
T1 - Improved shrinkage estimation of squared multiple correlation coefficient and squared cross-validity coefficient
AU - Shieh, Gwowen
PY - 2008/4
Y1 - 2008/4
N2 - 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.
AB - 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.
KW - Bias
KW - Maximum likelihood estimator
KW - Mean square error
KW - Multiple linear regression
KW - Shrinkage estimator
UR - http://www.scopus.com/inward/record.url?scp=40249116687&partnerID=8YFLogxK
U2 - 10.1177/1094428106292901
DO - 10.1177/1094428106292901
M3 - Article
AN - SCOPUS:40249116687
SN - 1094-4281
VL - 11
SP - 387
EP - 407
JO - Organizational Research Methods
JF - Organizational Research Methods
IS - 2
ER -