Details

Autor(en) / Beteiligte

• Cadre, Benoît
• Klutchnikoff, Nicolas
• Massiot, Gaspar

Titel

Minimax regression estimation for Poisson coprocess

Ist Teil von

• Probability and statistics, 2017, Vol.21, p.138-158

Ort / Verlag

Les Ulis: EDP Sciences

Erscheinungsjahr

2017

Link zum Volltext

Quelle

EZB Free E-Journals

Beschreibungen/Notizen

• 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.