On Stein's Method of Moments and Generalized Score Matching

TL;DR

This paper connects Stein's method of moments with generalized score matching, enabling the derivation of estimators with improved properties by extending the Stein class within the method of moments framework.

Contribution

It introduces a unified framework that extends Stein's method to generalized method of moments, simplifying the choice of weight functions for score matching estimators.

Findings

Unified framework for Stein's method and generalized score matching

Derivation of estimators with optimal properties

Extension of Stein class to generalized method of moments

Abstract

We show that a special case of method of moment estimator derived from the Stein class coincides with the class of generalized score matching estimator. Choosing a suitable weight function for generalized score matching is not straightforward. However, by placing it within the method of moment framework we can alleviate this problem by extending the Stein class to generalized method of moments. As a consequence we can work with a number of functions and hence derive generalized score matching estimators with optimal properties.