Dispersal density estimation across scales
The Annals of Statistics · 2023 · Volume 51 · Issue 3
Abstract
We consider a space structured population model generated by two-point clouds: a homogeneous Poisson process M with intensity n→∞ 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 σ−1f(·/σ). Based on a realisation of M and N, we study the nonparametric estimation of f and the estimation of the physical scale parameter σ>0 simultaneously for all regimes σ=σn. We establish that the optimal rates of convergence do not depend monotonously on the scale and we construct minimax estimators accordingly whether σ 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.
Keywords
60G57, 62G05, 62G07, 62M30, Deconvolution, dispersal models, Nonparametric estimation and minimax theory, Point processes, statistical inference across scales
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