Asymptotic approximation of the likelihood of stationary determinantal point processes
针对连续行列式点过程的最大似然估计难以直接计算的问题，提出一种新的渐近似然逼近方法，不限于矩形窗口、计算更快且无需调参，并给出估计量渐近方差的显式公式，模拟研究显示其优于常用替代方法。
Abstract Continuous determinantal point processes (DPPs) are a class of repulsive point processes on with many statistical applications. Although an explicit expression of their density is known, it is too complicated to be used directly for maximum likelihood estimation. In the stationary case, an approximation using Fourier series has been suggested, but it is limited to rectangular observation windows and no theoretical results support it. In this contribution, we investigate a different way to approximate the likelihood by looking at its asymptotic behavior when the observation window grows toward . This new approximation is not limited to rectangular windows, is faster to compute than the previous one, does not require any tuning parameter, and some theoretical justifications are provided. It moreover provides an explicit formula for estimating the asymptotic variance of the associated estimator. The performances are assessed in a simulation study on standard parametric models on and compare favorably to common alternative estimation methods for continuous DPPs.