Volume 19, 2015
|Page(s)||251 - 267|
|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
2 IRMAR, Ensai, CNRS, UEB, Campus de Ker Lann, Avenue Robert Schuman, 35170 Bruz, France
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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