For a Poisson point process , Itô’s famous chaos expansion implies that every square integrable regression function with covariate can be decomposed as a sum of multiple stochastic integrals called chaos. In this paper, we consider the case where can be decomposed as a sum of chaos. In the spirit of Cadre and Truquet [ESAIM: PS 19 (2015) 251–267], we introduce a semiparametric estimate of based on i.i.d. copies of the data. We investigate the asymptotic minimax properties of our estimator when is known. We also propose an adaptive procedure when is unknown.
Accepté le :
DOI : 10.1051/ps/2017004
Mots clés : Functional statistic, poisson point process, regression estimate, minimax estimation
@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://www.numdam.org/articles/10.1051/ps/2017004/} }
TY - JOUR AU - Cadre, Benoît AU - Klutchnikoff, Nicolas AU - Massiot, Gaspar TI - Minimax regression estimation for Poisson coprocess JO - ESAIM: Probability and Statistics PY - 2017 SP - 138 EP - 158 VL - 21 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps/2017004/ DO - 10.1051/ps/2017004 LA - en ID - PS_2017__21__138_0 ER -
%0 Journal Article %A Cadre, Benoît %A Klutchnikoff, Nicolas %A Massiot, Gaspar %T Minimax regression estimation for Poisson coprocess %J ESAIM: Probability and Statistics %D 2017 %P 138-158 %V 21 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ps/2017004/ %R 10.1051/ps/2017004 %G en %F PS_2017__21__138_0
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://www.numdam.org/articles/10.1051/ps/2017004/
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