Improvements on Cross-Validation: The 632+ Bootstrap Method

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 c...

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Veröffentlicht in:	Journal of the American Statistical Association Jg. 92; H. 438; S. 548 - 560
Hauptverfasser:	Efron, Bradley, Tibshirani, Robert
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Alexandria, VA Taylor & Francis Group 01.06.1997 American Statistical Association
Schlagworte:	Bootstrap resampling Classification Cross-validation bootstrap Error rates Estimation bias Estimation methods Estimators Exact sciences and technology Mathematics Multivariate analysis Nonparametric inference Point estimators Prediction rule Probability and statistics Sciences and techniques of general use Simulation training Standard deviation Standard error Statistical methods Statistical variance Statistics Theory and Methods Error estimation Error prediction Asymptotic behavior Prediction Samplings Error rate Non parametric method Cross validation Discriminant function Prediction rule Classification Classification problem Bootstrap Numerical simulation Fisher function
ISSN:	0162-1459, 1537-274X
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Abstract	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.
AbstractList	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.
Author	Tibshirani, Robert Efron, Bradley
Author_xml	– sequence: 1 givenname: Bradley surname: Efron fullname: Efron, Bradley organization: Department of Statistics , Stanford University – sequence: 2 givenname: Robert surname: Tibshirani fullname: Tibshirani, Robert organization: Department of Preventive Medicine and Biostatistics , University of Toronto
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Cites_doi	10.1080/00401706.1974.10489157 10.1080/01621459.1986.10478291 10.2307/2336519 10.1080/01621459.1975.10479865 10.1002/0471725293 10.1109/TPAMI.1987.4767957 10.1016/0167-8655(86)90035-8 10.1214/aos/1176344552 10.1016/0167-8655(85)90049-2 10.2307/1403680 10.1080/01621459.1983.10477973 10.1214/aos/1176349027 10.1007/978-1-4899-4541-9
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Keywords	Error estimation Error prediction Asymptotic behavior Prediction Samplings Error rate Non parametric method Cross validation Discriminant function Prediction rule Classification Classification problem Bootstrap Numerical simulation Fisher function
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SubjectTerms	Bootstrap resampling Classification Cross-validation bootstrap Error rates Estimation bias Estimation methods Estimators Exact sciences and technology Mathematics Multivariate analysis Nonparametric inference Point estimators Prediction rule Probability and statistics Sciences and techniques of general use Simulation training Standard deviation Standard error Statistical methods Statistical variance Statistics Theory and Methods
Title	Improvements on Cross-Validation: The 632+ Bootstrap Method
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