Stein operators allow to characterise probability distributions via differential operators. We use these characterisations 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 maximum likelihood estimator.

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，为严格平稳且遍历过程的边缘参数获得了一类新的点估计量。这些所谓的Stein估计量满足一致性、渐近正态性等经典优良性质。由于算子形式通常较为简单，我们在标准方法（如（伪）最大似然估计）需要数值计算才能获得估计值的场景中，得到了显式估计量。此外，通过该方法可以从大量检验函数类中进行选择，从而显著改进矩估计量。对于若干概率分布，我们能够确定在独立同分布情形下渐近表现接近有效性的估计量。进一步地，对于独立同分布观测，我们得到了能产生渐近有效估计量的数据依赖函数，并给出了收敛于最大似然估计量的显式Stein估计量序列。