%0 Journal Article %1 copas_regression_1983 %A Copas, J. B %D 1983 %J Journal of the Royal Statistical Society. Series B (Methodological) %K Bayes, Empirical bias-variance cited, highly multiple regression tradeoff, %N 3 %P 311 -- 354 %T Regression, prediction and shrinkage %U http://www.jstor.org/stable/2345402 %V 45 %X The fit of a regression predictor to new data is nearly always worse than its fit to the original data. Anticipating this shrinkage leads to Stein-type predictors which, under certain assumptions, give a uniformly lower prediction mean squared error than least squares. Shrinkage can be particularly marked when stepwise fitting is used: the shrinkage is then closer to that expected of the full regression rather than of the subset regression actually fitted. Preshrunk predictors for selected subsets are proposed and tested on a number of practical examples. Both multiple and binary (logistic) regression models are considered.

@article{copas_regression_1983, abstract = {The fit of a regression predictor to new data is nearly always worse than its fit to the original data. Anticipating this shrinkage leads to Stein-type predictors which, under certain assumptions, give a uniformly lower prediction mean squared error than least squares. Shrinkage can be particularly marked when stepwise fitting is used: the shrinkage is then closer to that expected of the full regression rather than of the subset regression actually fitted. Preshrunk predictors for selected subsets are proposed and tested on a number of practical examples. Both multiple and binary (logistic) regression models are considered.}, added-at = {2017-01-09T13:57:26.000+0100}, author = {Copas, J. B}, biburl = {https://www.bibsonomy.org/bibtex/29375488271ebfa13d041bfad35e95542/yourwelcome}, interhash = {d102edcd4300bc1107b75b17477851c8}, intrahash = {9375488271ebfa13d041bfad35e95542}, issn = {0035-9246}, journal = {Journal of the Royal Statistical Society. Series B (Methodological)}, keywords = {Bayes, Empirical bias-variance cited, highly multiple regression tradeoff,}, language = {English}, month = jan, number = 3, pages = {311 -- 354}, timestamp = {2017-01-09T14:01:11.000+0100}, title = {Regression, prediction and shrinkage}, url = {http://www.jstor.org/stable/2345402}, urldate = {2016-06-16}, volume = 45, year = 1983 }