Dispersal density estimation across scales
研究在空间结构化种群模型中，基于两代点过程数据，同时非参数估计扩散密度函数和物理尺度参数，发现最优收敛速率随尺度非单调变化，并构建了极小极大估计量。
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.