Journal ArticleDOI
Improvements of jackknife confidence limit methods
David Hinkley,Bo-Cheng Wet +1 more
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In this article, Edgeworth expansion is applied to studentized parameter estimates when the standard error has been computed by a jackknife method and adjustments to the usual jackknife confidence limit formulae are obtained.Abstract:
SUMMARY Edgeworth expansion is applied to studentized parameter estimates when the standard error has been computed by a jackknife method. Adjustments to the usual jackknife confidence limit formulae are obtained. This approach is contrasted with a bootstrap approach in numerical illustrations for estimation of a ratio. Jackknife methods are nonparametric methods for estimating the bias and standard error of an estimate T. Approximate confidence limits for the estimand can be found by using a large-sample normal approximation for T. Somewhat curiously, little is known about possible improvements to the normal approximation in this context, although improvements based on Edgeworth expansions are familiar in other problems. In this paper we show that Edgeworth expansion methods can be applied in the jackknife context. Numerical results for a particular application raise the possibility that the resulting improvements of jackknife methods can be matched by a suitable use of bootstrap methods (Efron, 1982).read more
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To Smooth or Not to Smooth?: Bias and Efficiency in fMRI Time-Series Analysis
Karl J. Friston,Oliver Josephs,Eric Zarahn,Andrew P. Holmes,Stéphanie Rouquette,Jean-Baptiste Poline +5 more
TL;DR: It is shown that: (i) Whitening strategies can result in profound bias and are therefore probably precluded in parametric fMRI data analyses and (ii) Band-pass filtering, and implicitly smoothing, has an important role in protecting against inferential bias.
Journal ArticleDOI
Prepivoting to reduce level error of confidence sets
TL;DR: In this article, the root of the confidence set is transformed by its estimated bootstrap cumulative distribution function, and the transformation of a confidence set root by the estimated distribution function can be iterated one or more times with smaller error than do confidence sets based on the original root.
Journal ArticleDOI
The bootstrap: To smooth or not to smooth?
Bernard W. Silverman,G. A. Young +1 more
TL;DR: In this paper, the authors consider the use of the smoothed bootstrap and the standard bootstrap for estimating properties of unknown distributions such as the sampling error of parameter estimates, and they develop criteria for determining whether it is advantageous to use the smoothed bootstrap rather than the traditional bootstrap.
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Efficient bootstrap simulation
TL;DR: In this article, deux ideas for renforcer a simulation are presented: 1) equilibrer les echantillons simules, 2) faire un usage explicite des approximations which ne demandent pas de simulation.
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Effect of bias estimation on coverage accuracy of bootstrap confidence intervals for a probability density
TL;DR: In this article, the authors use the percentile-t approach to construct confidence intervals for nonparametric density estimation and derive formulae for bandwidths which are optimal in terms of coverage accuracy, assuming a given number of derivatives of the unknown density.
References
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Book
The jackknife, the bootstrap, and other resampling plans
TL;DR: The Delta Method and the Influence Function Cross-Validation, Jackknife and Bootstrap Balanced Repeated Replication (half-sampling) Random Subsampling Nonparametric Confidence Intervals as mentioned in this paper.
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The jackknife-a review
TL;DR: In this paper, a review of the literature on the use of the jackknife technique in bias reduction and robust interval estimation is presented, and speculations and suggestions about future research are made.
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On the validity of the formal edgeworth expansion
TL;DR: In this paper, an asymptotic expansion of distributions of maximum likelihood estimators and, more generally, minimum contrast estimators of vector parameters under readily verifiable distributional assumptions is shown to be identical with a formal Edgeworth expansion of the distribution function of W.. This settles a conjecture of Wallace (1958).
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Inverting an Edgeworth Expansion
TL;DR: In this paper, a method for inverting a general Edgeworth expansion, so as to correct a statistic for the effects of non-normality, is presented, which is applied to the special case of the "Studentized" mean.
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Jackknife Approximations to Bootstrap Estimates
TL;DR: In this article, the first-order Edgeworth expansion estimate for the distribution of $n − 1/2 - T(F) was shown to be asymptotically equivalent to the corresponding bootstrap distribution estimate, up to and including terms of order $n− 1 2 -1/2.