The DOI matches its Crossref record; 14 of the 14 references it cites were found in a registry or an index.
The Jackknife and the Bootstrap for General Stationary Observations
Open accessAbstract
We extend the jackknife and the bootstrap method of estimating standard errors to the case where the observations form a general stationary sequence. We do not attempt a reduction to i.i.d. values. The jackknife calculates the sample variance of replicates of the statistic obtained by omitting each block of $l$ consecutive data once. In the case of the arithmetic mean this is shown to be equivalent to a weighted covariance estimate of the spectral density of the observations at zero. Under appropriate conditions consistency is obtained if $l = l(n) \rightarrow \infty$ and $l(n)/n \rightarrow 0$. General statistics are approximated by an arithmetic mean. In regular cases this approximation determines the asymptotic behavior. Bootstrap replicates are constructed by selecting blocks of length $l$ randomly with replacement among the blocks of observations. The procedures are illustrated by using the sunspot numbers and some simulated data.
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Bootstrap methods: another look at the jackknife
Efron, B. (1979) · The Annals of Statistics · doi:10.1214/aos/1176344552 · Cited by 17,602
Doob, J. L., & Doob, J. L. (1953) · CERN Document Server (European Organization for Nuclear Research) · Cited by 9,053
Efron, B., & Tibshirani, R. (1986) · Statistical Science · doi:10.1214/ss/1177013815 · Cited by 6,033
Approximation Theorems of Mathematical Statistics
Serfling, R. J. (1980) · Wiley Series in Probability and Statistics · doi:10.1002/9780470316481 · Cited by 5,851
Spectral Analysis and Time Series
Preston, D. B. (1983) · Technometrics · doi:10.1080/00401706.1983.10487866 · Cited by 5,011
Time Series: Data Analysis and Theory.
Koopmans, L. H., & Brillinger, D. R. (1976) · Journal of the American Statistical Association · doi:10.2307/2285347 · Cited by 2,637
Independent and stationary sequences of random variables
Ibragimov, I. A., Ліннік, Ю. В., & Kingmán, J. F. C. (1971) · Cited by 2,049
Some Asymptotic Theory for the Bootstrap
Bickel, P. J., & Freedman, D. A. (1981) · The Annals of Statistics · doi:10.1214/aos/1176345637 · Cited by 1,621
Time Series: Data Analysis and Theory.
Ray, W. D., & Brillinger, D. (1982) · Journal of the Royal Statistical Society. Series A (General) · doi:10.2307/2981427 · Cited by 1,342
Carlstein, E. (1986) · The Annals of Statistics · doi:10.1214/aos/1176350057 · Cited by 768
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Fast model-based estimation of ancestry in unrelated individuals
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The ENCODE Project Consortium (2007) · Nature · doi:10.1038/nature05874 · Cited by 5,223
A draft sequence of the Neandertal genome
Green, R. E., Krause, J., Briggs, A. W., Maricic, T., Stenzel, U., Kircher, M., Patterson, N., Li, H., Zhai, W., Fritz, M. H.-Y., et al. (2010) · Science · doi:10.1126/science.1188021 · Cited by 4,318
Politis, D. N., & Romano, J. P. (1994) · Journal of the American Statistical Association · doi:10.1080/01621459.1994.10476870 · Cited by 2,649
A Reality Check for Data Snooping
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Metadata
- Authors
- Kunsch, H. R.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 1989-09-01
- Volume
- 17
- Issue
- 3
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W2047694274
- Cited by
- 2,374
- References
- 14
- FWCI
- 11.03
- Type
- journal article
- Language
- en
- Open access
- bronze
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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