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.

翻译：我们获得了行列式点过程（DPPs）中整体参数L的最大似然估计量L_n的几乎必然强相合性及Berry-Esseen型误差界，从而强化并完善了Brunel、Moitra、Rigollet和Urschel [BMRU17] 开创的前期研究。本文开发了估计DPPs的数值算法并进行了模拟研究。最后，我们针对由2×2子矩阵构成的分块行列式矩阵，给出了最大似然估计量的显式公式与详细讨论，并将其与频率估计方法进行了比较。