The DOI matches its Crossref record; 5 of the 5 references it cites were found in a registry or an index.
Improvements on Cross-Validation: The 632+ Bootstrap Method
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.
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Cites
Breiman, L. (1996) · Machine Learning · doi:10.1007/bf00058655 · Cited by 16,325
A leisurely look at the bootstrap, the jackknife, and cross-validation
Efron, B., & Gong, G. (1983) · The American Statistician · doi:10.1080/00031305.1983.10483087 · Cited by 3,229
Self-citationThe Predictive Sample Reuse Method with Applications
Geisser, S. (1975) · Journal of the American Statistical Association · doi:10.1080/01621459.1975.10479865 · Cited by 2,748 · cited 1×
“Cross-validation (Geisser 1975; Stone 1974) avoids this problem by removing the data point to be predicted from the training set.”
MethodThe Relationship Between Variable Selection and Data Agumentation and a Method for Prediction
Allen, D. M. (1974) · Technometrics · doi:10.1080/00401706.1974.10489157 · Cited by 1,469 · cited 1×
“(A good general discussion can be found in McLachlan 1992; key references for cross-validation are Allen 1974 and Stone 1974, 1977.)”
BackgroundModel Selection Via Multifold Cross Validation
Zhang, P. (1993) · The Annals of Statistics · doi:10.1214/aos/1176349027 · Cited by 539
Cited by
Efron, B., Hastie, T., Johnstone, I., & Tibshirani, R. (2004) · The Annals of Statistics · doi:10.1214/009053604000000067 · Cited by 9,357
Self-citationA survey of cross-validation procedures for model selection
Arlot, S., & Celisse, A. (2010) · Statistics Surveys · doi:10.1214/09-ss054 · Cited by 3,522
Internal validation of predictive models
Steyerberg, E. W., Harrell, F. E., Borsboom, G. J. J. M., Eijkemans, M. J. C., Vergouwe, Y., & Habbema, J. D. F. (2001) · Journal of Clinical Epidemiology · doi:10.1016/s0895-4356(01)00341-9 · Cited by 2,746
A practical solution to the pervasive problems ofp values
Wagenmakers, E.-J. (2007) · Psychonomic Bulletin & Review · doi:10.3758/bf03194105 · Cited by 2,490
Bias in error estimation when using cross-validation for model selection
Varma, S., & Simon, R. (2006) · BMC Bioinformatics · doi:10.1186/1471-2105-7-91 · Cited by 2,485
“632 Bootstrap [10] and Bootstrap CV [11].”
Metadata
- Authors
- Efron, B., & Tibshirani, R.
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 1997-06
- Volume
- 92
- Issue
- 438
- Pages
- 548-560
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W2127314075
- Cited by
- 1,636
- References
- 5
- FWCI
- 8.12
- Type
- journal article
- Language
- en
- Open access
- closed
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