DISPERSAL DENSITY ESTIMATION ACROSS SCALES

Marc Hoffmann (1) , Mathias Trabs

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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]

Marc Hoffmann, Mathias Trabs. DISPERSAL DENSITY ESTIMATION ACROSS SCALES. 2022. ⟨hal-03913855⟩