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Adaptive estimating function inference for nonstationary determinantal point processes
Author(s) -
Lavancier Frédéric,
Poinas Arnaud,
Waagepetersen Rasmus
Publication year - 2021
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12440
Subject(s) - point process , mathematics , estimator , inference , truncation (statistics) , function (biology) , determinantal point process , point (geometry) , statistical inference , normality , algorithm , computer science , statistics , artificial intelligence , eigenvalues and eigenvectors , physics , geometry , random matrix , quantum mechanics , evolutionary biology , biology
Estimating function inference is indispensable for many common point process models where the joint intensities are tractable while the likelihood function is not. In this article, we establish asymptotic normality of estimating function estimators in a very general setting of nonstationary point processes. We then adapt this result to the case of nonstationary determinantal point processes, which are an important class of models for repulsive point patterns. In practice, often first‐ and second‐order estimating functions are used. For the latter, it is a common practice to omit contributions for pairs of points separated by a distance larger than some truncation distance, which is usually specified in an ad hoc manner. We suggest instead a data‐driven approach where the truncation distance is adapted automatically to the point process being fitted and where the approach integrates seamlessly with our asymptotic framework. The good performance of the adaptive approach is illustrated via simulation studies for non‐stationary determinantal point processes and by an application to a real dataset.