In Stein's method, one can characterize probability distributions with differential operators. We use these characterizations to obtain a new class of point estimators for i.i.d.\ observations. These so-called Stein 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 maximum likelihood estimation (MLE) 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. For several probability laws, we can determine an estimator that shows an asymptotic behaviour close to efficiency. Moreover, we retrieve data-dependent functions that result in asymptotically efficient estimators and give a sequence of explicit Stein estimators that converge to the MLE.

翻译：在斯坦因方法中，可以利用微分算子刻画概率分布。我们利用这些刻画方法为独立同分布观测提出了一类新的点估计量。这些所谓的斯坦因估计量具有相合性和渐近正态性等理想的经典性质。由于算子通常具有简单形式，我们能够在标准方法（如极大似然估计）需要数值计算才能获得估计值的情况下得到显式估计量。此外，我们的方法允许从一大类检验函数中进行选择，从而显著改进矩估计量。对于若干概率分布，我们可以确定渐近行为接近有效的估计量。同时，我们得到了能够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极大似然估计的显式斯坦因估计量。