DISPERSAL DENSITY ESTIMATION ACROSS SCALES

• 成果类型: Article
• 署名作者: Hoffmann, Marc; Trabs, Mathias
• 署名单位: Universite PSL; Universite Paris-Dauphine; Helmholtz Association; Karlsruhe Institute of Technology
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/23-AOS2290
• 发表日期: 2023
• 页码: 1258-1281
• 关键词: service time distribution; deconvolution; inference

摘要

We consider a space structured population model generated by two-point clouds: a homogeneous Poisson process M with intensity n -> infinity as a model for a parent generation together with a Cox point process N as offspring generation, with conditional intensity given by the convolution of M with a scaled dispersal density sigma(-1)f (center dot /sigma). Based on a realisation of M and N, we study the nonparametric estimation of f and the estimation of the physical scale parameter sigma > 0 simultaneously for all regimes sigma = sigma(n). We establish that the optimal rates of convergence do not depend monotonously on the scale and we construct minimax estimators accordingly whether sigma is known or considered as a nuisance, in which case we can estimate it and achieve asymptotic minimaxity by plug-in. The statistical reconstruction exhibits a competition between a direct and a deconvolution problem. Our study reveals in particular the existence of a least favorable intermediate inference scale, a phenomenon that seems to be new.