The DOI matches its Crossref record; 22 of the 22 references it cites were found in a registry or an index.
Predictive inference with the jackknife+
Open accessAbstract
This paper introduces the jackknife+, which is a novel method for constructing predictive confidence intervals. Whereas the jackknife outputs an interval centered at the predicted response of a test point, with the width of the interval determined by the quantiles of leave-one-out residuals, the jackknife+ also uses the leave-one-out predictions at the test point to account for the variability in the fitted regression function. Assuming exchangeable training samples, we prove that this crucial modification permits rigorous coverage guarantees regardless of the distribution of the data points, for any algorithm that treats the training points symmetrically. Such guarantees are not possible for the original jackknife and we demonstrate examples where the coverage rate may actually vanish. Our theoretical and empirical analysis reveals that the jackknife and the jackknife+ intervals achieve nearly exact coverage and have similar lengths whenever the fitting algorithm obeys some form of stability. Further, we extend the jackknife+ to $K$-fold cross validation and similarly establish rigorous coverage properties. Our methods are related to cross-conformal prediction proposed by Vovk (Ann. Math. Artif. Intell. 74 (2015) 9–28) and we discuss connections.
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Cites
Scikit-learn: Machine Learning in Python
Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., Blondel, M., Müller, A., Nothman, J., Louppe, G., et al. (2012) · arXiv · doi:10.48550/arxiv.1201.0490 · Cited by 71,016
Bootstrap methods: another look at the jackknife
Efron, B. (1979) · The Annals of Statistics · doi:10.1214/aos/1176344552 · Cited by 17,602
Cross validatory choice and assessment of statistical predictions
Stone, M. (1974) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1974.tb00994.x · Cited by 10,881
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 · cited 2×
“) Efron and Gong [9] provides an overview of the early literature on these types of methods.”
BackgroundThe 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 2×
“Several papers from this period include leave-one-out methods for assessing or calibrating predictive accuracy, similar to the predictive interval constructed in (1.2) above, for example, Stone [24], Geisser [10], Butler and Rothman [4], generally using the term “cross-validation” to refer to this approach.”
BackgroundInfluentialQUENOUILLE, M. H. (1956) · Biometrika · doi:10.1093/biomet/43.3-4.353 · Cited by 1,213
Distribution-Free Predictive Inference for Regression
Lei, J., G’Sell, M., Rinaldo, A., Tibshirani, R. J., & Wasserman, L. (2018) · Journal of the American Statistical Association · doi:10.1080/01621459.2017.1307116 · Cited by 1,049
Self-citationApproximate Tests of Correlation in Time-Series
Quenouille, M. H. (1949) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1949.tb00023.x · Cited by 872
Surprises in high-dimensional ridgeless least squares interpolation
Hastie, T., Montanari, A., Rosset, S., & Tibshirani, R. J. (2022) · The Annals of Statistics · doi:10.1214/21-aos2133 · Cited by 503
Self-citationConditional validity of inductive conformal predictors
Vovk, V. (2013) · Machine Learning · doi:10.1007/s10994-013-5355-6 · Cited by 225
Cited by
Distribution-free, Risk-controlling Prediction Sets
Bates, S., Angelopoulos, A., Lei, L., Malik, J., & Jordan, M. (2021) · Journal of the ACM · doi:10.1145/3478535 · Cited by 144
Angelopoulos, A. N., Bates, S., Zrnic, T., & Jordan, M. I. (2022) · Harvard Data Science Review · doi:10.1162/99608f92.16c71dad · Cited by 8
Zhu, M., Zecchin, M., Park, S., Guo, C., Feng, C., Popovski, P., & Simeone, O. (2025) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2025.3549222 · Cited by 6
The Peacemaker Fellowship and Urban Gun Violence in Richmond, California
Bruno, A., Darling-Hammond, S., Cabrera, J. R., Mujahid, M. S., & Corburn, J. (2026) · JAMA Network Open · doi:10.1001/jamanetworkopen.2026.31298 · Cited by 1
Metadata
- Authors
- Barber, R. F., Candès, E. J., Ramdas, A., & Tibshirani, R. J.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 2021-02-01
- Volume
- 49
- Issue
- 1
- Pages
- 486-507
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W2943913950
- Cited by
- 351
- References
- 22
- FWCI
- 28.72
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Barber, R. F., Candès, E. J., Ramdas, A., & Tibshirani, R. J. (2021). Predictive inference with the jackknife+. The Annals of Statistics. https://doi.org/10.1214/20-aos1965
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