Upper Bounds on the True Coverage of Bootstrap Percentile Type Confidence Intervals

1999 ◽  
Vol 53 (4) ◽  
pp. 362 ◽  
Author(s):  
Alan M. Polansky
Keyword(s):  
Confidence Intervals ◽  
Upper Bounds ◽  
Bootstrap Percentile

A note on coverage error of bootstrap confidence intervals for quantiles

1993 ◽  
Vol 114 (3) ◽  
pp. 517-531 ◽  
Author(s):  
D. De Angelis ◽  
Peter Hall ◽  
G. A. Young
Keyword(s):  
Confidence Intervals ◽  
Present Note ◽  
Normal Approximation ◽  
Poor Performance ◽  
Density Estimator ◽  
Bootstrap Confidence Intervals ◽  
Coverage Error ◽  
Bootstrap Percentile ◽  
Coverage Accuracy ◽  
Percentile Bootstrap

AbstractAn interesting recent paper by Falk and Kaufmann[11] notes, with an element of surprise, that the percentile bootstrap applied to construct confidence intervals for quantiles produces two-sided intervals with coverage error of size n−½, where n denotes sample size. By way of contrast, the error would be O(n−1) for two-sided intervals in more classical problems, such as intervals for means or variances. In the present note we point out that the relatively poor performance in the case of quantiles is shared by a variety of related procedures. The coverage accuracy of two-sided bootstrap intervals may be improved to o(n−½) by smoothing the bootstrap. We show too that a normal approximation method, not involving the bootstrap but incorporating a density estimator as part of scale estimation, can have coverage error O(n−1+∈), for arbitrarily small ∈ > 0. Smoothed and unsmoothed versions of bootstrap percentile-t are also analysed.

Percentile and Percentile-t Bootstrap Confidence Intervals: A Practical Comparison

2015 ◽  
Vol 4 (1) ◽  
Author(s):  
Christopher J. Elias
Keyword(s):  
Monte Carlo ◽  
Confidence Intervals ◽  
Monte Carlo Study ◽  
Bootstrap Confidence Intervals ◽  
Bootstrap Percentile

AbstractThis paper employs a Monte Carlo study to compare the performance of equal-tailed bootstrap percentile-

Confidence intervals on stratigraphic ranges: partial relaxation of the assumption of randomly distributed fossil horizons

Paleobiology ◽  
1994 ◽  
Vol 20 (4) ◽  
pp. 459-469 ◽  
Author(s):  
Charles R. Marshall
Keyword(s):  
Confidence Intervals ◽  
Fossil Record ◽  
Continuous Distribution ◽  
Random Processes ◽  
Upper Bounds ◽  
Restrictive Assumption ◽  
End Points ◽  
New Approach ◽  
Stratigraphic Position ◽  
Stratigraphic Ranges

The equations for calculating classical confidence intervals on the end points of stratigraphic ranges are based on the restrictive assumption of randomly distributed fossil finds. Herein, a method is presented for calculating confidence intervals on the end-points of stratigraphic ranges that partially relaxes this assumption: the method will work for any continuous distribution of gap sizes, not just those generated by random processes. The price paid for the generality of the new approach is twofold: (1) there are uncertainties associated with the sizes of the confidence intervals, and (2) for large confidence values (e.g., 95%) a rich fossil record is required to place upper bounds on the corresponding confidence intervals. This new method is not universal; like the method for calculating classical confidence intervals it is based on the assumption that there is no correlation between gap size and stratigraphic position. The fossil record of the Neogene Caribbean bryozoan Metrarabdotos is analyzed with the new approach. The equations developed here, like those for classical confidence intervals, should not be applied to stratigraphic ranges based on discrete sampling regimes, such as those typically established from deep-sea drilling cores, though there are exceptions to this rule.

scholarly journals Communicating Uncertainty in National Security Intelligence: Expert and Non-expert Interpretations of and Preferences for Verbal and Numeric Formats

2022 ◽  
Author(s):  
Daniel Irwin ◽  
David R. Mandel
Keyword(s):  
National Security ◽  
Confidence Intervals ◽  
Confidence Level ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Communication Preferences ◽  
Normative Expectation ◽  
Numeric Formats ◽  
Best Estimates

Organizations in several domains including national security intelligence communicate judgments under uncertainty using verbal probabilities (e.g., likely) instead of numeric probabilities (e.g., 75% chance), despite research indicating that the former have variable meanings across individuals. In the intelligence domain, uncertainty is also communicated using terms such as low, moderate, or high to describe the analyst’s confidence level. However, little research has examined how intelligence professionals interpret these terms and whether they prefer them to numeric uncertainty quantifiers. In two experiments (N = 481 and 624, respectively), uncertainty communication preferences of expert (n = 41 intelligence analysts inExperiment 1) and non-expert intelligence consumers were elicited. We examined which format participants judged to be more informative and simpler to process. We further tested whether participants treated probability and confidence as independent constructs and whether participants provided coherent numeric probability translations of verbal probabilities. Results showed that whereas most non-experts favored the numeric format, experts were about equally split, and most participants in both samples regarded the numeric format as more informative.Experts and non-experts consistently conflated probability and confidence. For instance, confidence intervals inferred from verbal confidence terms had a greater effect on the location of the estimate than the width of the estimate, contrary to normative expectation. Approximately ¼ of experts and over ½ of non-experts provided incoherent numeric probability translations of best estimates and lower and upper bounds when elicitations were spaced by intervening tasks.

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