{"ID":2840085,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.14551","arxiv_id":"2511.14551","title":"Minimax estimation of the structure factor of spatial point processes","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.","short_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 methodo...","url_abs":"https://arxiv.org/abs/2511.14551","url_pdf":"https://arxiv.org/pdf/2511.14551v1","authors":"[\"Gabriel Mastrilli\"]","published":"2025-11-18T14:53:45Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[]","has_code":false}