Issue |
ESAIM: PS
Volume 19, 2015
|
|
---|---|---|
Page(s) | 251 - 267 | |
DOI | https://doi.org/10.1051/ps/2014023 | |
Published online | 06 October 2015 |
Nonparametric regression estimation onto a Poisson point process covariate∗
1 IRMAR, ENS Rennes, CNRS, UEB, Campus
de Ker Lann, Avenue Robert
Schuman, 35170
Bruz,
France
cadre@ens-rennes.fr
2 IRMAR, Ensai, CNRS, UEB, Campus de
Ker Lann, Avenue Robert
Schuman, 35170
Bruz,
France
truquet@ensai.fr
Received:
13
March
2014
Revised:
18
September
2014
Let Y be a
real random variable and X be a Poisson point process. We investigate rates of
convergence of a nonparametric estimate r̂(x) of the regression function
r(x) = (Y|X = x), based on n independent copies of the
pair (X,Y).
The estimator r̂ is constructed using a Wiener–Itô decomposition of
r(X). In this infinite-dimensional
setting, we first obtain a finite sample bound on the expected squared difference
(r̂(X) - r(X))2. Then, under a condition ensuring that the model is
genuinely infinite-dimensional, we obtain the exact rate of convergence of ln
(r̂(X) - r(X))2.
Mathematics Subject Classification: 62G05 / 62G08
Key words: Regression estimation / Poisson point process / Wiener–Itô decomposition / rates of convergence
© EDP Sciences, SMAI 2015
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