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| - Nonparametric regression estimation onto a Poisson point process covariate
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| - 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) = \hbox{$\mathbb E$}( 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 \hbox{$\mathbb E$}( 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 \hbox{$\mathbb E$}( r̂(X) - r(X)) 2.
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| - © EDP Sciences, SMAI 2015
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