The DOI matches its Crossref record; 15 of the 15 references it cites were found in a registry or an index.
How Biased is the Apparent Error Rate of a Prediction Rule?
Abstract
A regression model is fitted to an observed set of data. How accurate is the model for predicting future observations? The apparent error rate tends to underestimate the true error rate because the data have been used twice, both to fit the model and to check its accuracy. We provide simple estimates for the downward bias of the apparent error rate. The theory applies to general exponential family linear models and general measures of prediction error. Special attention is given to the case of logistic regression on binary data, with error rates measured by the proportion of misclassified cases. Several connected ideas are compared: Mallows's Cp , cross-validation, generalized cross-validation, the bootstrap, and Akaike's information criterion.
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Cites
(2005) · Statistics for Biology and Health · doi:10.1007/0-387-27255-0_9 · Cited by 20,133
Generalized Cross-Validation as a Method for Choosing a Good Ridge Parameter
Golub, G. H., Heath, M., & Wahba, G. (1979) · Technometrics · doi:10.1080/00401706.1979.10489751 · Cited by 3,934
Craven, P., & Wahba, G. (1978) · Numerische Mathematik · doi:10.1007/bf01404567 · Cited by 3,388
Estimating the error rate of a prediction rule: improvement on cross-validation
Efron, B. (1983) · Journal of the American Statistical Association · doi:10.1080/01621459.1983.10477973 · Cited by 2,300
Self-citationMallows, C. L. (1995) · Technometrics · doi:10.1080/00401706.1995.10484370 · Cited by 2,083
McCullagh, P., & Nelder, J. A. (1983) · Springer eBooks · doi:10.1007/978-1-4899-3244-0 · Cited by 1,980
Mallows, C. L. (1973) · Technometrics · doi:10.2307/1267380 · Cited by 1,975
Smoothing noisy data with spline functions
Wahba, G. (1975) · Numerische Mathematik · doi:10.1007/bf01437407 · Cited by 1,443
An asymptotic equivalence of choice of model by cross validation and Akaike's criterion
Stone, M. (1977) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1977.tb01603.x · Cited by 1,286
The Efficiency of Logistic Regression Compared to Normal Discriminant Analysis
Efron, B. (1975) · Journal of the American Statistical Association · doi:10.1080/01621459.1975.10480319 · Cited by 567
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Cited by
Bayesian Measures of Model Complexity and Fit
Spiegelhalter, D. J., Best, N. G., Carlin, B. P., & Van Der Linde, A. (2002) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/1467-9868.00353 · Cited by 151
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
AIC model selection using Akaike weights
Wagenmakers, E.-J., & Farrell, S. (2004) · Psychonomic Bulletin & Review · doi:10.3758/bf03206482 · Cited by 2,684
Linear Model Selection by Cross-validation
Shao, J. (1993) · Journal of the American Statistical Association · doi:10.1080/01621459.1993.10476299 · Cited by 1,790
Metadata
- Authors
- Efron, B.
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 1986-06
- Volume
- 81
- Issue
- 394
- Pages
- 461-470
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W4249991467
- Cited by
- 587
- References
- 15
- FWCI
- 5.62
- Type
- journal article
- Language
- en
- Open access
- closed
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