DISPERSAL DENSITY ESTIMATION ACROSS SCALES
Résumé
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 −1 f (•/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 favourable intermediate inference scale, a phenomenon that seems to be new. * Corresponding author. † We thank our colleagues Marie Doumic and Alexander Goldenshluger for helpful discussions. We are grateful to the comments of three referees that convinced us to extend the results of a former version to the case of an unknown scale parameter. M.T. has been financially supported by DFG via the Heisenberg grant TR 1349/4-1.
Mots clés
AMS 2000 subject classifications: Primary 62G05
secondary 62G07 62M30 60G57 Nonparametric estimation and minimax theory point processes statistical inference across scales dispersal models deconvolution
secondary 62G07
62M30
60G57 Nonparametric estimation and minimax theory
point processes
statistical inference across scales
dispersal models
deconvolution
Domaines
Statistiques [math.ST]Origine | Fichiers produits par l'(les) auteur(s) |
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