Improvements on cross-validation: The .632+ bootstrap method

• 成果类型: Article
• 署名作者: Efron, B; Tibshirani, R
• 署名单位: University of Toronto
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.2307/2965703
• 发表日期: 1997
• 页码: 548-560
• 关键词: prediction rule; ERROR RATE; selection; regression; jackknife; CHOICE; MODEL

摘要

A training set of data has been used to construct a rule for predicting future responses. What is the error rate of this rule? This is an important question both for comparing models and for assessing a final selected model. The traditional answer to this question is given by cross-validation. The cross-validation estimate of prediction error is nearly unbiased but can be highly variable. Here we discuss bootstrap estimates of prediction error, which can be thought of as smoothed versions of cross-validation. We show that a particular bootstrap method the .632+ rule, substantially outperforms cross-validation in a catalog of 24 simulation experiments. Besides providing point estimates, we also consider estimating the variability of an error rate estimate. All of the results here are nonparametric and apply to any possible prediction rule; however, we study only classification problems with 0-1 loss in detail. Our simulations include ''smooth'' prediction rules Like Fisher's linear discriminant function and unsmooth ones like nearest neighbors.