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For parameter estimation of continuous and discrete distributions, we proposea generalization of the method of moments (MM), where Stein identities areutilized for improved estimation performance. The construction of theseStein-type MM-estimators makes use of a weight function as implied by anappropriate form of the Stein identity. Our general approach as well aspotential benefits thereof are first illustrated by the simple example of theexponential distribution. Afterward, we investigate the more sophisticatedtwo-parameter inverse Gaussian distribution and the two-parameternegative-binomial distribution in great detail, together with illustrativereal-world data examples. Given an appropriate choice of the respective weightfunctions, their Stein-MM estimators, which are defined by simple closed-formformulas and allow for closed-form asymptotic computations, exhibit a betterperformance regarding bias and mean squared error than competing estimators.

Generalized Moment Estimators based on Stein Identities