Stein operators allow to characterise probability distributions via differential operators. Based on these characterisations, we develop a new method of point estimation for marginal parameters of strictly stationary and ergodic processes, which we call \emph{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 allows to improve significantly on 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 excellent small sample behaviour, often outperforming the maximum likelihood estimator and other widely-used methods in terms of lower bias and mean squared error. We also illustrate the pertinence of our approach on a real data set related to rainfall modelisation.

翻译：斯坦算子允许通过微分算子刻画概率分布。基于这些刻画，我们针对严格平稳遍历过程的边缘参数开发了一种新的点估计方法，称为\emph{斯坦矩法}（SMOM）。这些SMOM估计量满足一致性、渐近正态性等经典优良性质。由于算子形式通常较为简单，我们在标准方法（如（伪）最大似然估计）需要数值计算才能获得估计值的场景中，得到了显式估计量。此外，通过本方法可从大量检验函数类中进行选择，从而显著改进矩估计的效果。进一步，对于独立同分布观测，我们得到了能产生渐近有效估计量的数据依赖函数，并给出了一列收敛于最大似然估计量的显式SMOM估计量。模拟研究表明，对于一系列重要的单变量连续概率分布，我们的SMOM估计量具有优异的小样本表现，在偏差与均方误差方面常优于最大似然估计量及其他广泛使用的方法。我们还在降雨建模相关的实际数据集上验证了本方法的适用性。