scholarly journals On the Admissibility of Simultaneous Bootstrap Confidence Intervals

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1212
Author(s):  
Xin Gao ◽  
Frank Konietschke ◽  
Qiong Li
Keyword(s):  
Confidence Intervals ◽  
Delta Method ◽  
Lasso Regression ◽  
Bootstrap Confidence Intervals ◽  
Simultaneous Confidence Intervals ◽  
Multiple Parameters ◽  
Joint Inference ◽  
Smoothed Bootstrap ◽  
Bootstrap Approach ◽  
Percentile Bootstrap

Simultaneous confidence intervals are commonly used in joint inference of multiple parameters. When the underlying joint distribution of the estimates is unknown, nonparametric methods can be applied to provide distribution-free simultaneous confidence intervals. In this note, we propose new one-sided and two-sided nonparametric simultaneous confidence intervals based on the percentile bootstrap approach. The admissibility of the proposed intervals is established. The numerical results demonstrate that the proposed confidence intervals maintain the correct coverage probability for both normal and non-normal distributions. For smoothed bootstrap estimates, we extend Efron’s (2014) nonparametric delta method to construct nonparametric simultaneous confidence intervals. The methods are applied to construct simultaneous confidence intervals for LASSO regression estimates.

Smoothed bootstrap confidence intervals with discrete data

1997 ◽  
Vol 26 (2) ◽  
pp. 163-176 ◽  
Author(s):  
Rudy Guerra ◽  
Alan M. Polansky ◽  
William R. Schucany
Keyword(s):  
Confidence Intervals ◽  
Discrete Data ◽  
Bootstrap Confidence Intervals ◽  
Smoothed Bootstrap

scholarly journals Evaluation of Bootstrap Confidence Intervals Using a New Non-Normal Process Capability Index

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 484 ◽  
Author(s):  
Gadde Srinivasa Rao ◽  
Mohammed Albassam ◽  
Muhammad Aslam
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Process Capability ◽  
Real Data ◽  
Process Capability Index ◽  
Monte Carlo Simulation Study ◽  
Bootstrap Confidence Intervals ◽  
Capability Index ◽  
Coverage Probabilities ◽  
Percentile Bootstrap

This paper assesses the bootstrap confidence intervals of a newly proposed process capability index (PCI) for Weibull distribution, using the logarithm of the analyzed data. These methods can be applied when the quality of interest has non-symmetrical distribution. Bootstrap confidence intervals, which consist of standard bootstrap (SB), percentile bootstrap (PB), and bias-corrected percentile bootstrap (BCPB) confidence interval are constructed for the proposed method. A Monte Carlo simulation study is used to determine the efficiency of newly proposed index Cpkw over the existing method by addressing the coverage probabilities and average widths. The outcome shows that the BCPB confidence interval is recommended. The methodology of the proposed index has been explained by using the real data of breaking stress of carbon fibers.

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.

scholarly journals Bootstrap Selector for the Smoothing Parameter of Beran’s Estimator

2021 ◽  
Vol 7 (1) ◽  
pp. 28
Author(s):  
Rebeca Peláez Suárez ◽  
Ricardo Cao Abad ◽  
Juan M. Vilar Fernández
Keyword(s):  
Confidence Intervals ◽  
Simulation Study ◽  
Smoothing Parameter ◽  
Bootstrap Confidence Intervals ◽  
Bootstrap Approximation ◽  
Mean Integrated Squared Error ◽  
Smoothed Bootstrap ◽  
Squared Error ◽  
Integrated Squared Error ◽  
The Mean

This work proposes a resampling technique to approximate the smoothing parameter of Beran’s estimator. It is based on resampling by the smoothed bootstrap and minimising the bootstrap approximation of the mean integrated squared error to find the bootstrap bandwidth. The behaviour of this method has been tested by simulation on several models. Bootstrap confidence intervals are also addressed in this research and their performance is analysed in the simulation study.

BOOTSTRAP CONFIDENCE INTERVALS FOR STEADY-STATE AVAILABILITY

2004 ◽  
Vol 21 (03) ◽  
pp. 407-419 ◽  
Author(s):  
JAE-HAK LIM ◽  
SANG WOOK SHIN ◽  
DAE KYUNG KIM ◽  
DONG HO PARK
Keyword(s):  
Steady State ◽  
Confidence Interval ◽  
Confidence Intervals ◽  
Coverage Probability ◽  
Average Length ◽  
Repairable System ◽  
Bootstrap Confidence Interval ◽  
Bootstrap Confidence Intervals ◽  
Bootstrap Methods ◽  
Percentile Bootstrap

Steady-state availability, denoted by A, has been widely used as a measure to evaluate the reliability of a repairable system. In this paper, we develop new confidence intervals for steady-state availability based on four bootstrap methods; standard bootstrap confidence interval, percentile bootstrap confidence interval, bootstrap-t confidence interval, and bias-corrected and accelerated confidence interval. We also investigate the accuracy of these bootstrap confidence intervals by calculating the coverage probability and the average length of intervals.

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