Mean-field limits have been used now as a standard tool in approximations, including for networks with a large number of nodes. Statistical inference on mean-filed models has attracted more attention recently mainly due to the rapid emergence of data-driven systems. However, studies reported in the literature have been mainly limited to continuous models. In this paper, we initiate a study of statistical inference on discrete mean-field models (or jump processes) in terms of a well-known and extensively studied model, known as the power-of-L, or the supermarket model, to demonstrate how to deal with new challenges in discrete models. We focus on system parameter estimation based on the observations of system states at discrete time epochs over a finite period. We show that by harnessing the weak convergence results developed for the supermarket model in the literature, an asymptotic inference scheme based on an approximate least squares estimation can be obtained from the mean-field limiting equation. Also, by leveraging the law of large numbers alongside the central limit theorem, the consistency of the estimator and its asymptotic normality can be established when the number of servers and the number of observations go to infinity. Moreover, numerical results for the power-of-two model are provided to show the efficiency and accuracy of the proposed estimator.

翻译：平均场极限现已成为近似分析的标准工具，包括用于具有大量节点的网络。近年来，由于数据驱动系统的迅速兴起，平均场模型的统计推断受到越来越多的关注。然而，文献中报道的研究主要局限于连续模型。本文以一类广为人知且被深入研究的模型——L次幂选择模型（或称超市模型）为例，首次对离散平均场模型（或跳跃过程）的统计推断展开研究，以阐明如何处理离散模型带来的新挑战。我们专注于基于有限时间段内离散时间点系统状态观测值的系统参数估计。研究表明，通过利用文献中为超市模型建立的弱收敛结果，可以从平均场极限方程推导出基于近似最小二乘估计的渐近推断方案。此外，借助大数定律与中心极限定理，当服务器数量和观测次数趋于无穷时，可以证明估计量的一致性和渐近正态性。最后，本文提供了二次幂选择模型的数值结果，以验证所提出估计量的效率和准确性。