Let be a real random variable and be a Poisson point process. We investigate rates of convergence of a nonparametric estimate of the regression function r(x) = (Y|X = x), based on independent copies of the pair . The estimator is constructed using a Wiener–Itô decomposition of . In this infinite-dimensional setting, we first obtain a finite sample bound on the expected squared difference (. Then, under a condition ensuring that the model is genuinely infinite-dimensional, we obtain the exact rate of convergence of ln(.
DOI : 10.1051/ps/2014023
Mots-clés : Regression estimation, Poisson point process, Wiener–Itô decomposition, rates of convergence
@article{PS_2015__19__251_0,
author = {Cadre, Beno{\^\i}t and Truquet, Lionel},
title = {Nonparametric regression estimation onto a {Poisson} point process covariate},
journal = {ESAIM: Probability and Statistics},
pages = {251--267},
publisher = {EDP-Sciences},
volume = {19},
year = {2015},
doi = {10.1051/ps/2014023},
mrnumber = {3412645},
zbl = {1392.62109},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ps/2014023/}
}
TY - JOUR AU - Cadre, Benoît AU - Truquet, Lionel TI - Nonparametric regression estimation onto a Poisson point process covariate JO - ESAIM: Probability and Statistics PY - 2015 SP - 251 EP - 267 VL - 19 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ps/2014023/ DO - 10.1051/ps/2014023 LA - en ID - PS_2015__19__251_0 ER -
%0 Journal Article %A Cadre, Benoît %A Truquet, Lionel %T Nonparametric regression estimation onto a Poisson point process covariate %J ESAIM: Probability and Statistics %D 2015 %P 251-267 %V 19 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ps/2014023/ %R 10.1051/ps/2014023 %G en %F PS_2015__19__251_0
Cadre, Benoît; Truquet, Lionel. Nonparametric regression estimation onto a Poisson point process covariate. ESAIM: Probability and Statistics, Tome 19 (2015), pp. 251-267. doi : 10.1051/ps/2014023. http://archive.numdam.org/articles/10.1051/ps/2014023/
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