Poisson intensity estimation with reproducing kernels. (English) Zbl 1387.62044

Flaxman, Seth; Teh, Yee Whye; Sejdinovic, Dino

Electron. J. Stat. 11, No. 2, 5081-5104 (2017).

A new computationally tractable reproducing kernel Hilbert space formulation is introduced for the inhomogeneous Poisson process. It is shown that the representer theorem still holds for the considered kernel \(\widetilde{k}\). The computation of \(\widetilde{k}\) is considered in two ways: when an explicit Mercer expansion is known and when access to the parametric form of the kernel is only available. To check the performances of the introduced approach, it is compared with the naïve one.

Reviewer: Miroslav M. Ristić (Niš)

MSC:

62G07	Density estimation
60G55	Point processes (e.g., Poisson, Cox, Hawkes processes)
46E22	Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)

Keywords:

nonparametric statistics; computational statistics; spatial statistics; intensity estimation; reproducing kernel Hilbert space; inhomogeneous Poisson processes