For parameter estimation of continuous and discrete distributions, we propose a generalization of the method of moments (MM), where Stein identities are utilized for improved estimation performance. The construction of these Stein-type MM-estimators makes use of a weight function as implied by an appropriate form of the Stein identity. Our general approach as well as potential benefits thereof are first illustrated by the simple example of the exponential distribution. Afterward, we investigate the more sophisticated two-parameter inverse Gaussian distribution and the two-parameter negative-binomial distribution in great detail, together with illustrative real-world data examples. Given an appropriate choice of the respective weight functions, their Stein-MM estimators, which are defined by simple closed-form formulas and allow for closed-form asymptotic computations, exhibit a better performance regarding bias and mean squared error than competing estimators.

翻译：针对连续分布与离散分布的参数估计问题，本文提出了一种矩估计法（MM）的推广形式，通过引入Stein恒等式提升估计性能。此类Stein型矩估计量的构造基于Stein恒等式特定形式所隐含的权重函数。我们首先以指数分布为例阐明该通用方法及其潜在优势，随后详细分析更具复杂性的双参数逆高斯分布与双参数负二项分布，并辅以实际数据案例说明。在合理选取相应权重函数的前提下，此类由闭合形式公式定义且支持闭合形式渐近计算的Stein矩估计量，在偏差与均方误差方面均优于竞争性估计量。