Stein's method of moments
基于施泰因算子，提出一种针对严格平稳遍历过程边际参数的点估计新方法，称为施泰因矩方法，其估计量具有相合性和渐近正态性，且在小样本下表现有竞争力。
Abstract Stein operators allow one to characterize probability distributions via differential operators. Based on these characterizations, we develop a new method of point estimation for marginal parameters of strictly stationary and ergodic processes, which we call Stein's Method of Moments (SMOM). These SMOM estimators satisfy the desirable classical properties such as consistency and asymptotic normality. As a consequence of the usually simple form of the operator, we obtain explicit estimators in cases where standard methods such as (pseudo‐) maximum likelihood estimation require a numerical procedure to calculate the estimate. In addition, with our approach, one can choose from a large class of test functions, which typically allows for improvements over the moment estimator. Moreover, for i.i.d. observations, we retrieve data‐dependent functions that result in asymptotically efficient estimators and give a sequence of explicit SMOM estimators that converge to the maximum likelihood estimator. Our simulation study demonstrates that for a number of important univariate continuous probability distributions, our SMOM estimators possess competitive small sample behavior, in comparison to the maximum likelihood estimator and other widely‐used methods in terms of bias and mean squared error. We also illustrate the pertinence of our approach on a real data set related to rainfall modelization.