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Journal ArticleDOI

Bootstrap Confidence Intervals

01 Sep 1996-Statistical Science (Institute of Mathematical Statistics)-Vol. 11, Iss: 3, pp 189-228
TL;DR: 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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Journal ArticleDOI
TL;DR: This note summarizes developments of the genepop software since its first description in 1995, and in particular those new to version 4.0: an extended input format, several estimators of neighbourhood size under isolation by distance, new estimators and confidence intervals for null allele frequency, and less important extensions to previous options.
Abstract: This note summarizes developments of the genepop software since its first description in 1995, and in particular those new to version 4.0: an extended input format, several estimators of neighbourhood size under isolation by distance, new estimators and confidence intervals for null allele frequency, and less important extensions to previous options. genepop now runs under Linux as well as under Windows, and can be entirely controlled by batch calls.

8,171 citations


Cites methods from "Bootstrap Confidence Intervals"

  • ...Approximate bootstrap confidence (ABC) intervals (DiCiccio & Efron 1996) for Dσ2 are computed, assuming that each locus is an independent realization of genealogical and mutation processes....

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Journal ArticleDOI
TL;DR: The mediation package implements a comprehensive suite of statistical tools for conducting causal mediation analysis in applied empirical research and implements a statistical method for dealing with multiple (causally dependent) mediators, which are often encountered in practice.
Abstract: In this paper, we describe the R package mediation for conducting causal mediation analysis in applied empirical research. In many scientific disciplines, the goal of researchers is not only estimating causal effects of a treatment but also understanding the process in which the treatment causally affects the outcome. Causal mediation analysis is frequently used to assess potential causal mechanisms. The mediation package implements a comprehensive suite of statistical tools for conducting such an analysis. The package is organized into two distinct approaches. Using the model-based approach, researchers can estimate causal mediation effects and conduct sensitivity analysis under the standard research design. Furthermore, the design-based approach provides several analysis tools that are applicable under different experimental designs. This approach requires weaker assumptions than the model-based approach. We also implement a statistical method for dealing with multiple (causally dependent) mediators, which are often encountered in practice. Finally, the package also offers a methodology for assessing causal mediation in the presence of treatment noncompliance, a common problem in randomized trials.

2,417 citations


Cites methods from "Bootstrap Confidence Intervals"

  • ...The bias-corrected and accelerated (BCa) intervals are computed if the argument is set to "bca" (see DiCiccio and Efron 1996, for the definition of the method)....

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Journal ArticleDOI
TL;DR: In this article, the authors address Ronkko and Evermann's criticisms of the Partial Least Squares (PLS) approach to structural equation modeling and conclude that PLS should continue to be used as an important statistical tool for management and organizational research, as well as other social science disciplines.
Abstract: This article addresses Ronkko and Evermann’s criticisms of the partial least squares (PLS) approach to structural equation modeling. We contend that the alleged shortcomings of PLS are not due to problems with the technique, but instead to three problems with Ronkko and Evermann’s study: (a) the adherence to the common factor model, (b) a very limited simulation designs, and (c) overstretched generalizations of their findings. Whereas Ronkko and Evermann claim to be dispelling myths about PLS, they have in reality created new myths that we, in turn, debunk. By examining their claims, our article contributes to reestablishing a constructive discussion of the PLS method and its properties. We show that PLS does offer advantages for exploratory research and that it is a viable estimator for composite factor models. This can pose an interesting alternative if the common factor model does not hold. Therefore, we can conclude that PLS should continue to be used as an important statistical tool for management and organizational research, as well as other social science disciplines.

1,906 citations

Journal ArticleDOI
TL;DR: A brief review of the psychometric literature on coefficient alpha is presented, followed by a practical alternative in the form of coefficient omega, to facilitate the shift from alpha to omega.
Abstract: Coefficient alpha is the most popular measure of reliability (and certainly of internal consistency reliability) reported in psychological research. This is noteworthy given the numerous deficiencies of coefficient alpha documented in the psychometric literature. This mismatch between theory and practice appears to arise partly because users of psychological scales are unfamiliar with the psychometric literature on coefficient alpha and partly because alternatives to alpha are not widely known. We present a brief review of the psychometric literature on coefficient alpha, followed by a practical alternative in the form of coefficient omega. To facilitate the shift from alpha to omega, we also present a brief guide to the calculation of point and interval estimates of omega using a free, open source software environment.

1,860 citations


Cites methods from "Bootstrap Confidence Intervals"

  • ...For example, Iacobucci andDuhachek (2003) provide a simplemethod of bootstrapping to obtain CIs for alpha.3 Bootstrapping involves repeated resampling with replacement from a sample to obtain an ‘empirical’ distribution of an estimator such as alpha (DiCiccio & Efron, 1996)....

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Journal ArticleDOI
TL;DR: This article reviews the common algorithms for resampling and methods for constructing bootstrap confidence intervals, together with some less well known ones, highlighting their strengths and weaknesses.
Abstract: Since the early 1980s, a bewildering array of methods for constructing bootstrap confidence intervals have been proposed. In this article, we address the following questions. First, when should bootstrap confidence intervals be used. Secondly, which method should be chosen, and thirdly, how should it be implemented. In order to do this, we review the common algorithms for resampling and methods for constructing bootstrap confidence intervals, together with some less well known ones, highlighting their strengths and weaknesses. We then present a simulation study, a flow chart for choosing an appropriate method and a survival analysis example.

1,416 citations

References
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Book
01 Jan 1993
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.
Abstract: This article presents bootstrap methods for estimation, using simple arguments. Minitab macros for implementing these methods are given.

37,183 citations

Journal ArticleDOI
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.
Abstract: We discuss the following problem given a random sample X = (X 1, X 2,…, X n) from an unknown probability distribution F, estimate the sampling distribution of some prespecified random variable R(X, F), on the basis of the observed data x. (Standard jackknife theory gives an approximate mean and variance in the case R(X, F) = \(\theta \left( {\hat F} \right) - \theta \left( F \right)\), θ some parameter of interest.) A general method, called the “bootstrap”, is introduced, and shown to work satisfactorily on a variety of estimation problems. The jackknife is shown to be a linear approximation method for the bootstrap. The exposition proceeds by a series of examples: variance of the sample median, error rates in a linear discriminant analysis, ratio estimation, estimating regression parameters, etc.

14,483 citations

Book
28 Oct 1997
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.
Abstract: This book gives a broad and up-to-date coverage of bootstrap methods, with numerous applied examples, developed in a coherent way with the necessary theoretical basis. Applications include stratified data; finite populations; censored and missing data; linear, nonlinear, and smooth regression models; classification; time series and spatial problems. Special features of the book include: extensive discussion of significance tests and confidence intervals; material on various diagnostic methods; and methods for efficient computation, including improved Monte Carlo simulation. Each chapter includes both practical and theoretical exercises. Included with the book is a disk of purpose-written S-Plus programs for implementing the methods described in the text. Computer algorithms are clearly described, and computer code is included on a 3-inch, 1.4M disk for use with IBM computers and compatible machines. Users must have the S-Plus computer application. Author resource page: http://statwww.epfl.ch/davison/BMA/

6,420 citations

Journal ArticleDOI
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.
Abstract: We consider the problem of setting approximate confidence intervals for a single parameter θ in a multiparameter family. The standard approximate intervals based on maximum likelihood theory, , can be quite misleading. In practice, tricks based on transformations, bias corrections, and so forth, are often used to improve their accuracy. The bootstrap confidence intervals discussed in this article automatically incorporate such tricks without requiring the statistician to think them through for each new application, at the price of a considerable increase in computational effort. The new intervals incorporate an improvement over previously suggested methods, which results in second-order correctness in a wide variety of problems. In addition to parametric families, bootstrap intervals are also developed for nonparametric situations.

2,870 citations

01 Jan 1987
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.
Abstract: We consider the problem of setting approximate confidence intervals for a single parameter 0 in a multiparameter family. The standard approximate intervals based on maximum likelihood theory, 8 2 &z(=), can be quite misleading. In practice, tricks based on transformations, bias corrections, and so forth, are often used to improve their accuracy. The bootstrap confidence intervals discussed in this article automatically incorporate such tricks without requiring the statistician to think them through for each new application, at the price of a considerable increase in computational effort. The new intervals incorporate an improvement over previously suggested methods, which results in second-order correctness in a wide variety of problems. In addition to parametric families, bootstrap intervals are also developed for nonparametric situations.

2,828 citations


"Bootstrap Confidence Intervals" refers background or methods in this paper

  • ...The equality of z0 and a in this context was demonstrated by Efron (1987)....

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  • ...References include Efron (1987), Hall (1988), DiCiccio (l984), DiCiccio and Romano (1995) and Efron and Tibshirani (1993)....

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  • ...In the relationships below we assume that θ̂ behaves asymptotically like a maximum likelihood estimator, with respect to a notional sample size n, as made explicit in (5.3) of Efron (1987)....

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  • ...The argument in Section 3 of Efron (1987) shows that in situation (2.5) there is another monotone transformation, say ξ = M θ and ξ̂ = M θ̂ , such that ξ̂ = ξ +W for all values of ξ, with W always having the same distribution....

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  • ...Section 10 of Efron (1987) shows that one-sixth the skewness of ˙̀ θ θ̂ evaluated at θ = θ̂, 3:10 â = SKEWθ=θ̂ ˙̀θ θ̂ /6; is an excellent estimate of a....

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