We revisit the problem of parameter estimation for discrete probability distributions with values in $\mathbb{Z}^d$. To this end, we adapt a technique called Stein's Method of Moments to discrete distributions which often gives closed-form estimators when standard methods such as maximum likelihood estimation (MLE) require numerical optimization. These new estimators exhibit good performance in small-sample settings which is demonstrated by means of a comparison to the MLE through simulation studies. We pay special attention to truncated distributions and show that the asymptotic behavior of our estimators is not affected by an unknown (rectangular) truncation domain.

翻译：我们重新审视了取值于$\mathbb{Z}^d$的离散概率分布的参数估计问题。为此，我们将一种称为斯坦因矩方法的技术应用于离散分布，该方法通常能在最大似然估计等标准方法需要数值优化时给出闭式估计器。通过与最大似然估计的模拟比较研究证明，这些新型估计器在小样本场景下表现出良好的性能。我们特别关注截断分布，并证明了未知（矩形）截断域不会影响我们估计器的渐近性质。