Minimax regression estimation for Poisson coprocess
نویسندگان
چکیده
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 (2015), 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. Index Terms — Functional statistic, Poisson point process, regression estimate, Minimax estimation AMS 2010 Classification — 62G08, 62H12, 62M30
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