Volume 21, 2017
|Page(s)||138 - 158|
|Published online||19 October 2017|
Minimax regression estimation for Poisson coprocess∗
1 IRMAR, ENS Rennes, CNRS, Campus de Ker Lann, Avenue Robert Schuman, 35170 Bruz, France.
2 IRMAR, Université de Rennes 2, CNRS, Campus Villejean, Place du recteur Henri le Moal, CS 24307, 35043 Rennes cedex, France.
Received: 29 November 2016
Revised: 2 March 2017
Accepted: 5 March 2017
For a Poisson point process X, Itô’s famous chaos expansion implies that every square integrable regression function r with covariate X can be decomposed as a sum of multiple stochastic integrals called chaos. In this paper, we consider the case where r can be decomposed as a sum of δ chaos. In the spirit of Cadre and Truquet [ESAIM: PS 19 (2015) 251–267], we introduce a semiparametric estimate of r based on i.i.d. copies of the data. We investigate the asymptotic minimax properties of our estimator when δ is known. We also propose an adaptive procedure when δ is unknown.
Mathematics Subject Classification: 62G08 / 62H12 / 62M30
Key words: Functional statistic / poisson point process / regression estimate / minimax estimation
© EDP Sciences, SMAI, 2017
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