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Bootstrap Confidence Intervals

Thomas J. DiCiccio, +1 more
- 01 Sep 1996 - 
- Vol. 11, Iss: 3, pp 189-228
TLDR
Bootstrap methods for estimating confidence intervals have been surveyed in this article, with a focus on improving the accuracy of the standard confidence intervals in a way that allows routine application even to very complicated problems.
Abstract
This article surveys bootstrap methods for producing good approximate confidence intervals. The goal is to improve by an order of magnitude upon the accuracy of the standard intervals $\hat{\theta} \pm z^{(\alpha)} \hat{\sigma}$, in a way that allows routine application even to very complicated problems. Both theory and examples are used to show how this is done. The first seven sections provide a heuristic overview of four bootstrap confidence interval procedures: $BC_a$, bootstrap-t , ABC and calibration. Sections 8 and 9 describe the theory behind these methods, and their close connection with the likelihood-based confidence interval theory developed by Barndorff-Nielsen, Cox and Reid and others.

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Citations
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Should I stay or should I go? The influence of temperature and sex on predator-induced responses in newts

TL;DR: It is concluded that temperature and sex are important determinants of a newt's defensive repertoire and suggests both asymmetric selection regimes and an impact of environmental change in newt populations.
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Predicting implementation cost contingencies for residential construction projects in flood-prone areas

TL;DR: This study attempts to predict implementation cost contingencies for residential construction projects in flood-prone areas using non-parametric bootstrap method, which could be useful for project cost budgeting and/or effective cost management.
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Estimating moose abundance in linear subarctic habitats in low snow conditions with distance sampling and a kernel estimator

TL;DR: In this article, a line-transect distance sampling approach was used to estimate the abundance of moose along the tributaries of the lower Kuskokwim River within the Yukon Delta National Wildlife Refuge.
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A comparison of some confidence intervals for the mean quality-adjusted lifetime with censored data

TL;DR: Simulation studies are employed to compare the performance of these methods with various sample sizes and different censoring rates, and methods with the best performance will be identified.
References
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Book

An introduction to the bootstrap

TL;DR: This article presents bootstrap methods for estimation, using simple arguments, with Minitab macros for implementing these methods, as well as some examples of how these methods could be used for estimation purposes.
Journal ArticleDOI

Bootstrap Methods: Another Look at the Jackknife

TL;DR: In this article, the authors discuss the problem of estimating the sampling distribution of a pre-specified random variable R(X, F) on the basis of the observed data x.
Book

Bootstrap Methods and Their Application

TL;DR: In this paper, a broad and up-to-date coverage of bootstrap methods, with numerous applied examples, developed in a coherent way with the necessary theoretical basis, is given, along with a disk of purpose-written S-Plus programs for implementing the methods described in the text.
Journal ArticleDOI

Better Bootstrap Confidence Intervals

TL;DR: In this article, the authors consider the problem of setting approximate confidence intervals for a single parameter θ in a multiparameter family, and propose a method to automatically incorporate transformations, bias corrections, and so on.

Beiter Bootstrap Confidence Intervals

Bradley Efron
TL;DR: In this article, the authors consider the problem of setting approximate confidence intervals for a single parameter 0 in a multiparameter family, and propose the bootstrap confidence intervals that automatically incorporate transformations, bias corrections, and so forth.