  Stein operators allow to characterise probability distributions via
differential operators. Based on these characterisations, we develop a new
method of point estimation for marginal parameters of strictly stationary and
ergodic processes, which we call Stein's Method of Moments (SMOM). These SMOM
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. Moreover, for i.i.d. observations, we retrieve data-dependent
functions that result in asymptotically efficient estimators and give a
sequence of explicit SMOM estimators that converge to the maximum likelihood
estimator. Our simulation study demonstrates that for a number of important
univariate continuous probability distributions our SMOM estimators possess
excellent small sample behaviour, often outperforming the maximum likelihood
estimator and other widely-used methods in terms of lower bias and mean squared
error.
