Generalized Moment Estimators based on Stein Identities

TL;DR

This paper introduces a generalized method of moments estimator using Stein identities, which improves parameter estimation accuracy for various distributions by leveraging weight functions for better bias and mean squared error performance.

Contribution

It develops a novel Stein-based generalized method of moments estimator that provides closed-form formulas and improved estimation accuracy over traditional methods.

Findings

Stein-MM estimators outperform traditional estimators in bias and MSE.

The approach applies to exponential, inverse Gaussian, and negative-binomial distributions.

Closed-form formulas enable straightforward asymptotic analysis.

Abstract

For parameter estimation of continuous and discrete distributions, we propose a generalization of the method of moments (MM), where Stein identities are utilized for improved estimation performance. The construction of these Stein-type MM-estimators makes use of a weight function as implied by an appropriate form of the Stein identity. Our general approach as well as potential benefits thereof are first illustrated by the simple example of the exponential distribution. Afterward, we investigate the more sophisticated two-parameter inverse Gaussian distribution and the two-parameter negative-binomial distribution in great detail, together with illustrative real-world data examples. Given an appropriate choice of the respective weight functions, their Stein-MM estimators, which are defined by simple closed-form formulas and allow for closed-form asymptotic computations, exhibit a better performance regarding bias and mean squared error than competing estimators.