Asymptotic properties of maximum likelihood estimators for determinantal point processes
Statistics Theory
2024-07-10 v3 Statistics Theory
Abstract
We obtain the almost sure strong consistency and the Berry-Esseen type bound for the maximum likelihood estimator Ln of the ensemble L for determinantal point processes (DPPs), strengthening and completing previous work initiated in Brunel, Moitra, Rigollet, and Urschel [BMRU17]. Numerical algorithms of estimating DPPs are developed and simulation studies are performed. Lastly, we give explicit formula and a detailed discussion for the maximum likelihood estimator for blocked determinantal matrix of two by two submatrices and compare it with the frequency method.
Keywords
Cite
@article{arxiv.2307.00733,
title = {Asymptotic properties of maximum likelihood estimators for determinantal point processes},
author = {Yaozhong Hu and Haiyi Shi},
journal= {arXiv preprint arXiv:2307.00733},
year = {2024}
}