标题： 离散分布的新闭式估计量 显示英文标题

标题： New closed-form estimators for discrete distributions

摘要： 我们重新研究了在$\mathbb{Z}^d$上取值的离散概率分布的参数估计问题。 为此，我们适应了一种称为Stein方法矩的技巧，用于离散分布，通常在标准方法如最大似然估计（MLE）需要数值优化时，可以给出闭式估计量。 这些新的估计量在小样本情况下表现出良好的性能，这是通过与MLE进行模拟研究比较来证明的。 我们特别关注截断分布，并表明我们的估计量的渐近行为不受未知（矩形）截断域的影响。 显示英文摘要

摘要： 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.