Moment convergence of the generalized maximum composite likelihood estimators for determinantal point processes

TL;DR

This paper introduces a two-step generalized maximum composite likelihood estimator for determinantal point processes, demonstrating its moment convergence and potential for model selection in stationary DPPs.

Contribution

It proposes a novel two-step generalized composite likelihood estimator for DPPs and proves its moment convergence under stationarity.

Findings

Estimator exhibits moment convergence under stationarity.

Results enable development of information criteria for model selection.

Applicable to any order of joint intensities in DPPs.

Abstract

The maximum composite likelihood estimator for parametric models of determinantal point processes (DPPs) is discussed. Since the joint intensities of these point processes are given by determinant of positive definite kernels, we have the explicit form of the joint intensities for every order. This fact enables us to consider the generalized maximum composite likelihood estimator for any order. This paper introduces the two step generalized composite likelihood estimator and shows the moment convergence of the estimator under a stationarity. Moreover, our results can yield information criteria for statistical model selection within DPPs.