Geodesic
Bootstrapping the shorth for regression
ESAIM: Probability and Statistics, Tome 10 (2006), pp. 216-235

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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 n 1/2 -rate to a gaussian law and that the estimator of the centre converges at the n 1/3 -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.

DOI : 10.1051/ps:2006007
Classification : 62E20, 62G05, 62G08, 62G09
Keywords: brownian motion with parabolic drift, bootstrap, location of maximum, shorth 
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     author = {Durot, C\'ecile and Thi\'ebot, Karelle},
     title = {Bootstrapping the shorth for regression},
     journal = {ESAIM: Probability and Statistics},
     pages = {216--235},
     publisher = {EDP-Sciences},
     volume = {10},
     year = {2006},
     doi = {10.1051/ps:2006007},
     mrnumber = {2219341},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps:2006007/}
}
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Durot, Cécile; Thiébot, Karelle. Bootstrapping the shorth for regression. ESAIM: Probability and Statistics, Tome 10 (2006), pp. 216-235. doi: 10.1051/ps:2006007

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