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Zheng, L. Bootstrap Confidence Intervals. Encyclopedia. Available online: https://encyclopedia.pub/entry/60136 (accessed on 22 September 2026).
Zheng L. Bootstrap Confidence Intervals. Encyclopedia. Available at: https://encyclopedia.pub/entry/60136. Accessed September 22, 2026.
Zheng, Lionel. "Bootstrap Confidence Intervals" Encyclopedia, https://encyclopedia.pub/entry/60136 (accessed September 22, 2026).
Zheng, L. (2026, September 18). Bootstrap Confidence Intervals. In Encyclopedia. https://encyclopedia.pub/entry/60136
Zheng, Lionel. "Bootstrap Confidence Intervals." Encyclopedia. Web. 18 September, 2026.
Bootstrap Confidence Intervals
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Bootstrap confidence intervals are interval estimates of a population parameter constructed by resampling the observed data with replacement, rather than by relying on an analytic sampling distribution or an assumed parametric form [1]. In the bootstrap procedure, a large number of bootstrap replicates are drawn from the original sample, each replicate having the same size as the sample and containing observations drawn uniformly at random with replacement [2]. The statistic of interest is recomputed on each replicate, yielding the bootstrap distribution of the statistic; this distribution serves as an empirical estimate of the sampling distribution from which standard errors, bias estimates, and confidence intervals are derived [1]. Several interval constructions exist: the percentile interval uses the empirical quantiles of the bootstrap distribution; the basic bootstrap interval reflects the difference between the estimate and its bootstrap quantiles; and bias-corrected and accelerated intervals adjust for bias and skewness in the bootstrap distribution [3]. Bootstrap confidence intervals are distinguished from analytic intervals by their reliance on computationally intensive resampling and by their weaker assumptions about the underlying distribution [2].

bootstrap confidence interval bootstrap resampling percentile bootstrap statistical uncertainty quantification

References

  1. B. Efron; Bootstrap Methods: Another Look at the Jackknife. Ann. Stat. 1979, 7, 1-26. [CrossRef]
  2. Bradley Efron; R.J. Tibshirani. An Introduction to the Bootstrap; Taylor & Francis: London, United Kingdom, 1994. [CrossRef]
  3. Efron, B. Better Bootstrap Confidence Intervals. Journal of the American Statistical Association 1987, 82, 171–185. [CrossRef]
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