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Regression, prediction and shrinkage. (English) Zbl 0532.62048

In this paper many of the ideas pertaining to prediction and shrinkage in the regression model have been tied together. The term shrinkage refers to the amount by which prospective or validation fit (fit to new data) falls short of retrospective fit (fit to the original data). Thus the fit of a regression predictor to new data is always worse than its fit to the original data. Shrinkage is greatly affected by empirical model selection. Shrinkage is closer to that expected to the full regression rather than of the subset regression actually fitted when stepwise regression is used. Anticipating this shrinkage leads to Stein-type predictors which give a uniformly lower prediction mean square error than least squares.
In this paper the author proposes preshrunk predictors for selected subsets. There are four illustrated practical examples in which these proposed predictors are tested. Both multiple and binary regression models are discussed.
Reviewer: D.V.Chopra

MSC:

62J99 Linear inference, regression
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