Minimax estimation of the structure factor of spatial point processes

Gabriel Mastrilli

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arXiv · 2511.14551

Minimax estimation of the structure factor of spatial point processes

Gabriel Mastrilli

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Abstract

We investigate the problem of estimating the structure factor, or spectra, of stationary spatial point processes. In the first part, we establish a minimax lower bound for this estimation problem, using an approach tailored to second-order properties of spatial point processes. Although not the main focus, this methodology also extends naturally to a minimax lower bound for the estimation of the pair correlation function of spatial point processes. In the second part, we construct a multitaper estimator that achieves the optimal rate of convergence in squared risk. Under a Brillinger-mixing condition, we further establish a chi-square-type concentration bound. Finally, we propose a data-driven procedure for selecting the number of tapers, supported by an oracle inequality, and we demonstrate the practical effectiveness of the method through numerical experiments.

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Gabriel Mastrilli. 2025-11-18. Minimax estimation of the structure factor of spatial point processes. https://arxiv.org/abs/2511.14551

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