Stein operators allow to characterise probability distributions via differential operators. We use these characterizations to obtain a new class of point estimators for marginal parameters of strictly stationary and ergodic processes. 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 (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. For several probability laws, we can determine an estimator that shows an asymptotic behaviour close to efficiency in the i.i.d.\ case. Moreover, for i.i.d. observations, 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：Stein算子允许通过微分算子刻画概率分布。我们利用这些刻画为严格平稳遍历过程的边际参数获得了一类新的点估计量。这些所谓的Stein估计量具有理想经典性质，如相合性和渐近正态性。由于算子形式通常简洁，在标准方法（如（伪）极大似然估计）需要数值计算步骤来获得估计量的情形下，我们得到了显式估计量。此外，通过我们的方法，可以从大量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，我们能够确定一种估计量，该估计量在独立同分布情形下展现出接近有效性的渐近行为。进一步地，对于独立同分布观测，我们重构了可生成渐近有效估计量的数据依赖函数，并给出了一个收敛到MLE的显式Stein估计量序列。