Estimation of the squared crossvalidity coefficient in the context of best subset regression

A monte carlo study was conducted to examine the performance of several strategies for estimating the squared cross-validity coefficient of a sample regres-sion equation in the context of best subset regression. Data were simulated for populations and experimental designs likely to be encountered in practice. The re-sults indicated that a formula presented by Stein (1960) could be expected to yield estimates as good as or better than cross-validation, or several other for-mula estimators, for the populations considered. Fur-ther, the results suggest that sample size may play a much greater role in validity estimation in subset se-lection than is true in situations where selection has not occurred. Index terms: Best subset regression, Cross-validity coefficient, Multiple regression, Predic