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The Jackknife Estimate of Variance
Abstract
Tukey's jackknife estimate of variance for a statistic $S(X_1, X_2, \cdots, X_n)$ which is a symmetric function of i.i.d. random variables $X_i$, is investigated using an ANOVA-like decomposition of $S$. It is shown that the jackknife variance estimate tends always to be biased upwards, a theorem to this effect being proved for the natural jackknife estimate of $\operatorname{Var} S(X_1, X_2, \cdots, X_{n-1})$ based on $X_1, X_2, \cdots, X_n$.
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Citations
Cited by
Efron, B., & Tibshirani, R. (1986) · Statistical Science · doi:10.1214/ss/1177013815 · Cited by 6,033
Self-citationSaltelli, A., Annoni, P., Azzini, I., Campolongo, F., Ratto, M., & Tarantola, S. (2010) · Computer Physics Communications · doi:10.1016/j.cpc.2009.09.018 · Cited by 3,623
Estimation and Inference of Heterogeneous Treatment Effects using Random Forests
Wager, S., & Athey, S. (2018) · Journal of the American Statistical Association · doi:10.1080/01621459.2017.1319839 · Cited by 2,917
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-citationSynthetic Difference-in-Differences
Arkhangelsky, D., Athey, S., Hirshberg, D. A., Imbens, G. W., & Wager, S. (2021) · American Economic Review · doi:10.1257/aer.20190159 · Cited by 1,518
Metadata
- Authors
- Efron, B., & Stein, C.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 1981-05-01
- Volume
- 9
- Issue
- 3
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W1992068214
- Cited by
- 1,436
- References
- 0
- FWCI
- 10.01
- Type
- journal article
- Language
- en
- Open access
- closed
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- Efron, B., & Stein, C. (1981). The Jackknife Estimate of Variance. The Annals of Statistics. https://doi.org/10.1214/aos/1176345462
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