Journal Article10.1002/CJS.5550340104
On the bootstrap in cube root asymptotics
Christian Léger,Brenda MacGibbon +1 more
TL;DR: In this article, the authors study the application of the bootstrap to a class of estimators which converge at a non-standard rate to a nonstandard distribution and provide a theoretical framework to study its asymptotic behavior.
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Abstract: The authors study the application of the bootstrap to a class of estimators which converge at a nonstandard rate to a nonstandard distribution. They provide a theoretical framework to study its asymptotic behaviour. A simulation study shows that in the case of an estimator such as Chernoff's estimator of the mode, usually the basic bootstrap confidence intervals drastically undercover while the percentile bootstrap intervals overcover. This is a rare instance where basic and percentile confidence intervals, which have exactly the same length, behave in a very different way. In the case of Chernoff's estimator, if the distribution is symmetric, it is possible to bootstrap from a smooth symmetric estimator of the distribution for which the basic bootstrap confidence intervals will have the claimed coverage probability while the percentile bootstrap interval will have an asymptotic coverage of 1!
A propos du bootstrap pour des estimateurs convergeant a la vitesse racine cubique
Les auteurs etudient l'application du bootstrap a une classe d'estimateurs qui convergent a une vitesse et vers une loi non standard. Ils presentent un cadre theorique pour l'etude de son comportement asymptotique. Une simulation demontre que dans le cas d'un estimateur du mode de Chernoff, la probabilite de couverture de l'intervalle de confiance bootstrap de base est grandement inferieure au niveau prescrit, alors que celle des intervalles de type percentile depasse le niveau prescrit. C'est un rare cas ou les intervalles de confiance de base et percentile ont un comportement si different malgre des longueurs identiques. Dans le cas de l'estimateur de Chernoff, si la distribution est symetrique, il est possible d'appliquer le bootstrap a partir d'un estimateur lisse et symetrique de la distribution qui menera a des intervalles bootstrap de base dont la probabilite de couverture asymptotique sera la bonne, alors que celle de l'intervalle percentile convergera vers 1!
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Citations
Inconsistency of bootstrap: The Grenander estimator
TL;DR: In this paper, the authors investigate the consistency of different bootstrap methods for constructing confidence intervals in the class of estimators that converge at rate $n^{1/3}. But they focus on the Grenander estimator, the nonparametric maximum likelihood estimator of an unknown nonincreasing density function on $[0,\infty)
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Quantile regression approach to conditional mode estimation
TL;DR: In this paper, an estimator derived from a linear quantile regression model and developed asymptotic distributional theory for the estimator was proposed and applied to predicting the net hourly electrical energy output using Combined Cycle Power Plant Data.
Fractals with point impact in functional linear regression
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TL;DR: In this article, a point impact linear regression model is proposed for continuous stochastic processes, where the trajectory of a continuous stocho-process when evaluated at a sensitive time point is associated with scalar response.
Bootstrap diagnostics and remedies
TL;DR: In this article, the authors present a Web of Science Record created on 2006-04-21, modified on 2017-05-12 for a paper entitled "Reference STAT-ARTICLE-2006-007:
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The Bootstrap in Threshold Regression
TL;DR: In this paper, the authors developed a general procedure to check the bootstrap validity in M-estimation and applied the procedure in discontinuous threshold regression to show the inconsistency of the nonparametric bootstrap for inference on the threshold point.
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