New closed-form estimators for discrete distributions

TL;DR

This paper introduces new closed-form estimators for discrete distributions using Stein's Method of Moments, offering advantages in small samples and robustness to truncation, compared to traditional MLE methods.

Contribution

The paper adapts Stein's Method of Moments to discrete distributions, providing closed-form estimators that perform well in small samples and are unaffected by unknown truncation domains.

Findings

Estimators outperform MLE in small-sample scenarios.

Estimators are robust to unknown rectangular truncation.

Simulation studies confirm good performance.

Abstract

We revisit the problem of parameter estimation for discrete probability distributions with values in $\mathbb{Z}^d$. To this end, we adapt a technique called Stein's Method of Moments to discrete distributions which often gives closed-form estimators when standard methods such as maximum likelihood estimation (MLE) require numerical optimization. These new estimators exhibit good performance in small-sample settings which is demonstrated by means of a comparison to the MLE through simulation studies. We pay special attention to truncated distributions and show that the asymptotic behavior of our estimators is not affected by an unknown (rectangular) truncation domain.