Bootstrapping the shorth for regression

Cécile Durot; Karelle Thiébot

ESAIM: Probability and Statistics (2006)

  • Volume: 10, page 216-235
  • ISSN: 1292-8100

Abstract

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The paper is concerned with the asymptotic distributions of estimators for the length and the centre of the so-called η-shorth interval in a nonparametric regression framework. It is shown that the estimator of the length converges at the n1/2-rate to a Gaussian law and that the estimator of the centre converges at the n1/3-rate to the location of the maximum of a Brownian motion with parabolic drift. Bootstrap procedures are proposed and shown to be consistent. They are compared with the plug-in method through simulations.

How to cite

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Durot, Cécile, and Thiébot, Karelle. "Bootstrapping the shorth for regression." ESAIM: Probability and Statistics 10 (2006): 216-235. <http://eudml.org/doc/249738>.

@article{Durot2006,
abstract = { The paper is concerned with the asymptotic distributions of estimators for the length and the centre of the so-called η-shorth interval in a nonparametric regression framework. It is shown that the estimator of the length converges at the n1/2-rate to a Gaussian law and that the estimator of the centre converges at the n1/3-rate to the location of the maximum of a Brownian motion with parabolic drift. Bootstrap procedures are proposed and shown to be consistent. They are compared with the plug-in method through simulations. },
author = {Durot, Cécile, Thiébot, Karelle},
journal = {ESAIM: Probability and Statistics},
keywords = {Brownian motion with parabolic drift; bootstrap; location of maximum; shorth.; shorth},
language = {eng},
month = {5},
pages = {216-235},
publisher = {EDP Sciences},
title = {Bootstrapping the shorth for regression},
url = {http://eudml.org/doc/249738},
volume = {10},
year = {2006},
}

TY - JOUR
AU - Durot, Cécile
AU - Thiébot, Karelle
TI - Bootstrapping the shorth for regression
JO - ESAIM: Probability and Statistics
DA - 2006/5//
PB - EDP Sciences
VL - 10
SP - 216
EP - 235
AB - The paper is concerned with the asymptotic distributions of estimators for the length and the centre of the so-called η-shorth interval in a nonparametric regression framework. It is shown that the estimator of the length converges at the n1/2-rate to a Gaussian law and that the estimator of the centre converges at the n1/3-rate to the location of the maximum of a Brownian motion with parabolic drift. Bootstrap procedures are proposed and shown to be consistent. They are compared with the plug-in method through simulations.
LA - eng
KW - Brownian motion with parabolic drift; bootstrap; location of maximum; shorth.; shorth
UR - http://eudml.org/doc/249738
ER -

References

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