The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.
Bootstrap confidence intervals for a class of parametric problems
Abstract
We consider the following class of problems: having observed a multivariate normal data vector y with unknown mean vector η, covariance matrix the identity, find an approximate confidence interval for ø = t(η), a real-valued function of η. A simple geometric construction is given which leads to highly accurate solutions. This construction shows that the standard approximation based on maximum likelihood theory, ø7plusmn;σz(α), can be quite misleading when ø is nonlinear in η. We discuss bootstrap-based confidence intervals which remove most of the error in the standard approximation, at the expense of considerably more calculation. The bootstrap intervals are invariant under transformation of both y and η, and so they automatically produce accurate solutions in problems which can be transformed to multivariate normality, without requiring knowledge of the normalizing transformation.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
The Jackknife, the Bootstrap and Other Resampling Plans
Efron, B. (1982) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9781611970319 · Cited by 8,120
Self-citation
Cited by
Efron, B., & Tibshirani, R. (1986) · Statistical Science · doi:10.1214/ss/1177013815 · Cited by 6,033
Self-citationAn approximately unbiased test of phylogenetic tree selection
Shimodaira, H. (2002) · Systematic Biology · doi:10.1080/10635150290069913 · Cited by 2,791
A review of bootstrap confidence intervals
Diciccio, T. J., & Romano, J. P. (1988) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1988.tb01732.x · Cited by 314
Bootstrap confidence intervals and bootstrap approximations
Diciccio, T., & Tibshirani, R. (1987) · Journal of the American Statistical Association · doi:10.1080/01621459.1987.10478409 · Cited by 95
Temporal patterns in daily measurements of inorganic and organic speciated PM2.5 in Denver
Dutton, S. J., Rajagopalan, B., Vedal, S., & Hannigan, M. P. (2010) · Atmospheric Environment · doi:10.1016/j.atmosenv.2009.06.006 · Cited by 33
Metadata
- Authors
- EFRON, B.
- Venue
- Biometrika
- Publisher
- Oxford University Press (OUP)
- Published
- 1985
- Volume
- 72
- Issue
- 1
- Pages
- 45-58
- ISSN
- 0006-3444 (ISSN-L)
- 1464-3510
- OpenAlex
- W2161772062
- Cited by
- 289
- References
- 1
- FWCI
- 8.48
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Bootstrap confidence intervals for a class of parametric problems. https://app.cochat.ai/papers/10.1093/biomet/72.1.45
- The paper
- EFRON, B. (1985). Bootstrap confidence intervals for a class of parametric problems. Biometrika. https://doi.org/10.1093/biomet/72.1.45
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
