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Bootstrap Confidence Intervals: History
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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

Statistical Methods and Inference •  Statistics and Probability •  Mathematics •  Physical Sciences

References

  1. B. Efron; Bootstrap Methods: Another Look at the Jackknife. Ann. Stat. 1979, 7, 1-26, 10.1214/aos/1176344552.
  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, 10.1080/01621459.1987.10478410.
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