Minimax regression estimation for Poisson coprocess

Cadre, Benoît; Klutchnikoff, Nicolas; Massiot, Gaspar

doi:10.1051/ps/2017004

Cadre, Benoît ¹ ; Klutchnikoff, Nicolas ² ; Massiot, Gaspar ²

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.

ESAIM: Probability and Statistics, Tome 21 (2017), pp. 138-158.

Résumé

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.

Reçu le : 2016-11-29
Accepté le : 2017-03-05

MR Zbl

DOI : 10.1051/ps/2017004

Classification : 62G08, 62H12, 62M30
Mots clés : Functional statistic, poisson point process, regression estimate, minimax estimation

Affiliations des auteurs :

Cadre, Benoît ¹ ; Klutchnikoff, Nicolas ² ; Massiot, Gaspar ²

@article{PS_2017__21__138_0,
     author = {Cadre, Beno{\^\i}t and Klutchnikoff, Nicolas and Massiot, Gaspar},
     title = {Minimax regression estimation for {Poisson} coprocess},
     journal = {ESAIM: Probability and Statistics},
     pages = {138--158},
     publisher = {EDP-Sciences},
     volume = {21},
     year = {2017},
     doi = {10.1051/ps/2017004},
     mrnumber = {3716123},
     zbl = {1395.62086},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/ps/2017004/}
}

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Cadre, Benoît; Klutchnikoff, Nicolas; Massiot, Gaspar. Minimax regression estimation for Poisson coprocess. ESAIM: Probability and Statistics, Tome 21 (2017), pp. 138-158. doi : 10.1051/ps/2017004. http://archive.numdam.org/articles/10.1051/ps/2017004/

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