Robust and Efficient Estimation for a Discrete Distribution Using L2 Optimization

TL;DR

This paper introduces a new estimation method for the Poisson distribution's rate parameter using a Cramer-von Mises type optimization, demonstrating robustness and favorable performance over traditional methods.

Contribution

It adapts a continuous distribution estimation technique to discrete distributions and thoroughly investigates its statistical properties.

Findings

The proposed estimator has desirable asymptotic properties.

Simulation shows it outperforms maximum likelihood estimation.

The method is robust to model deviations.

Abstract

This paper proposes a novel method to estimate the rate parameter of the Poisson distribution. The proposed method employs the Cramer-von Mises type optimization which has been commonly used in estimating parameters of continuous distributions. Upon obtaining the estimator through the proposed method, its desirable properties such as asymptotic distribution and robustness are rigorously investigated. Simulation studies serve to demonstrate that the proposed method compares favorably with other well-celebrated methods including the maximum likelihood method.