Journal
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
Volume 99, Issue 467, Pages 619-632Publisher
AMER STATISTICAL ASSOC
DOI: 10.1198/016214504000000692
Keywords
C-p; degrees of freedom; nonparametric estimates; parametric bootstrap; Rao-Blackwellization; SURE
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Having constructed a data-based estimation rule, perhaps a logistic regression or a classification tree, the statistician would like to know its performance as a predictor of future cases. There are two main theories concerning prediction error: (I) penalty methods such as C-p, Akaike's information criterion, and Stein's unbiased risk estimate that depend on the covariance between data points and their corresponding predictions; and (2) cross-validation and related nonparametric bootstrap techniques. This article concerns the connection between the two theories. A Rao-Blackwell type of relation is derived in which nonparametric methods such as cross-validation are seen to be randomized versions of their covariance penalty counterparts. The model-based penalty methods offer substantially better accuracy, assuming that the model is believable.
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