The `Exact' Bootstrap Approach to Confidence Intervals for the Relative Difference Statistic

1987 ◽  
Vol 36 (4) ◽  
pp. 345 ◽  
Author(s):  
A. Kinsella
Keyword(s):  
Confidence Intervals ◽  
Relative Difference ◽  
Difference Statistic ◽  
Bootstrap Approach

Confidence intervals for the ratio of two independent Poisson rates: Parametric bootstrap, modified asymptotic, and approximate-estimate approaches

2019 ◽  
Vol 29 (8) ◽  
pp. 2140-2150
Author(s):  
Mahmood Kharrati-Kopaei ◽  
Raziye Dorosti-Motlagh
Keyword(s):  
Confidence Intervals ◽  
Coverage Probability ◽  
Ad Hoc ◽  
Rare Events ◽  
Average Length ◽  
Parametric Bootstrap ◽  
Asymptotic Results ◽  
Approximate Estimate ◽  
Bootstrap Approach ◽  
Estimate Method

We propose four confidence intervals for the ratio of two independent Poisson rates. We apply a parametric bootstrap approach, two modified asymptotic results, and we propose an ad-hoc approximate-estimate method to construct confidence intervals. We justify the correctness of the proposed methods asymptotically in the case of non-rare events (when the Poisson rates are large). We also compare the proposed confidence intervals with some recommended ones in the case of rare events (when the Poisson rates are small) via an extensive simulation study. The results show that the proposed modified asymptotic and the approximate-estimate confidence intervals perform reasonably well in terms of coverage probability and average length.

scholarly journals SLACK AND NET TECHNICAL EFFICIENCY MEASUREMENT: A BOOTSTRAP APPROACH

2005 ◽  
Vol 04 (03) ◽  
pp. 395-410 ◽  
Author(s):  
J. RICHMOND
Keyword(s):  
Confidence Intervals ◽  
Technical Efficiency ◽  
Small Component ◽  
Empirical Application ◽  
Use Of Resources ◽  
Bootstrap Techniques ◽  
Bootstrap Approach ◽  
Efficiency Estimation ◽  
Downward Bias ◽  
Cautious Interpretation

Statistical properties of DEA methods for efficiency estimation are poorly understood and currently the best way forward must be to use bootstrap techniques. The article seeks to extend bootstrap methods to allow investigation of the properties of estimates of inefficiencies due to the slack in the use of resources as well as technical efficiency. In an empirical application, it is found that inefficiency due to slack is a small component of the overall inefficiency and that the DEA technical efficiency estimates have a small downward bias, with confidence intervals that are wide enough to suggest cautious interpretation.

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.

Bootstrap Identification of Confidence Intervals for the Non-Linear DoE Model

2015 ◽  
Vol 712 ◽  
pp. 11-16
Author(s):  
Jacek Pietraszek ◽  
Norbert Radek ◽  
Małgorzata Stojek ◽  
Andrii Goroshko ◽  
Maciej Kołomycki
Keyword(s):  
Normal Distribution ◽  
Response Surface ◽  
Confidence Intervals ◽  
Analytical Solutions ◽  
Design Of Experiment ◽  
Uncertainty Estimation ◽  
Response Surface Model ◽  
Surface Model ◽  
Bootstrap Approach ◽  
Non Linear

Design of experiment (DoE) is a methodology widely used in an industry and an academia. However the fundamentals of DoE are well known since first articles of R.A. Fisher, the uncertainty estimation is still the investigated issue due to the fact that non-linear outcome functions do not preserve the normal distribution. The analytical solutions are known only for a very limited number of transformation. Authors propose to involve a bootstrap approach to estimate the outcome uncertainty of the response surface model.

scholarly journals Estimating confidence intervals for cerebral autoregulation: a parametric bootstrap approach

2021 ◽  
Author(s):  
Jack Edward Douglas Bryant ◽  
Anthony A Birch ◽  
Ronney B Panerai ◽  
Dragana Nikolic ◽  
Diederik O Bulters ◽  
...  
Keyword(s):  
Confidence Intervals ◽  
Cerebral Autoregulation ◽  
Parametric Bootstrap ◽  
Bootstrap Approach

scholarly journals Estimation of Past Demographic Parameters From the Distribution of Pairwise Differences When the Mutation Rates Vary Among Sites: Application to Human Mitochondrial DNA

Genetics ◽  
1999 ◽  
Vol 152 (3) ◽  
pp. 1079-1089 ◽  
Author(s):  
Stefan Schneider ◽  
Laurent Excoffier
Keyword(s):  
Mitochondrial Dna ◽  
Confidence Intervals ◽  
Mutation Rates ◽  
Demographic Parameters ◽  
Human Mitochondrial Dna ◽  
Estimated Parameters ◽  
Bootstrap Approach ◽  
Population Sizes ◽  
Pairwise Differences ◽  
Infinite Sites Model

AbstractDistributions of pairwise differences often called “mismatch distributions” have been extensively used to estimate the demographic parameters of past population expansions. However, these estimations relied on the assumption that all mutations occurring in the ancestry of a pair of genes lead to observable differences (the infinite-sites model). This mutation model may not be very realistic, especially in the case of the control region of mitochondrial DNA, where this methodology has been mostly applied. In this article, we show how to infer past demographic parameters by explicitly taking into account a finite-sites model with heterogeneity of mutation rates. We also propose an alternative way to derive confidence intervals around the estimated parameters, based on a bootstrap approach. By checking the validity of these confidence intervals by simulations, we find that only those associated with the timing of the expansion are approximately correctly estimated, while those around the population sizes are overly large. We also propose a test of the validity of the estimated demographic expansion scenario, whose proper behavior is verified by simulation. We illustrate our method with human mitochondrial DNA, where estimates of expansion times are found to be 10–20% larger when taking into account heterogeneity of mutation rates than under the infinite-sites model.

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