The paper is concerned with the asymptotic distributions of estimators for the length and the centre of the so-called -shorth interval in a nonparametric regression framework. It is shown that the estimator of the length converges at the -rate to a gaussian law and that the estimator of the centre converges at the -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.
Mots clés : brownian motion with parabolic drift, bootstrap, location of maximum, shorth
@article{PS_2006__10__216_0, 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://www.numdam.org/articles/10.1051/ps:2006007/} }
TY - JOUR AU - Durot, Cécile AU - Thiébot, Karelle TI - Bootstrapping the shorth for regression JO - ESAIM: Probability and Statistics PY - 2006 SP - 216 EP - 235 VL - 10 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps:2006007/ DO - 10.1051/ps:2006007 LA - en ID - PS_2006__10__216_0 ER -
Durot, Cécile; Thiébot, Karelle. Bootstrapping the shorth for regression. ESAIM: Probability and Statistics, Tome 10 (2006), pp. 216-235. doi : 10.1051/ps:2006007. http://www.numdam.org/articles/10.1051/ps:2006007/
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