Stein's Method of Moments

Abstract

Stein operators allow one to characterize probability distributions via differential operators. Based on these characterizations, we develop a new method of point estimation for parameters, 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 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 typically allows for improvements over the moment estimator. We visit parametric estimation problems in Euclidean space, on the hypersphere as well as on random graphs. This is based on joint work with Robert Gaunt and Yvik Swan.

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