Abstract

When a population is suspected to comprise several homogeneous subpopulations, each adequately modeled by a standard parametric distribution, the overall distribution can be described as a finite mixture. While finite mixture models are well-motivated and find broad applications, they present numerous technical challenges in developing valid and effective statistical inference procedures. A notable gap exists in our current understanding concerning the convergence rate for estimating the mixing distribution, particularly when the order of the finite mixture model is overspecified based on independent and identically distributed (iid) observations. The best attainable minimax rate for the subpopulation distribution with a single parameter, in cases where the order is overspecified by one, was initially believed to be $n^{-1/4}$ but has been revised to $n^{-1/6}$. In this presentation, we will elucidate some findings pertaining to the moment estimator and its minimax convergence rate.