Dispersal density estimation across scales
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We consider a space structured population model generated by two point clouds: a homogeneous Poisson process M=∑_jδ_X_j with intensity of order n→∞ as a model for a parent generation together with a Cox point process N=∑_jδ_Y_j as offspring generation, with conditional intensity of order M∗(σ^-1f(·/σ)), where ∗ denotes convolution, f is the so-called dispersal density, the unknown parameter of interest, and σ>0 is a physical scale parameter. Based on a realisation of M and N, we study the nonparametric estimation of f, for several regimes σ=σ_n. We establish that the optimal rates of convergence do not depend monotonously on the scale σ and construct minimax estimators accordingly. Depending on σ, the reconstruction problem exhibits a competition between a direct and a deconvolution problem. Our study reveals in particular the existence of a least favourable intermediate inference scale.
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