Closed-form estimators for an exponential family derived from likelihood equations

TL;DR

This paper introduces closed-form estimators for exponential family distributions, enhances them with bootstrap bias reduction, and validates their effectiveness through Monte Carlo simulations.

Contribution

It provides novel closed-form estimators for exponential family parameters along with a bootstrap bias reduction method, supported by simulation results.

Findings

Bootstrap bias-reduced estimators outperform standard ones

Simulations confirm the estimators' accuracy and efficiency

Proposed methods are computationally straightforward

Abstract

In this paper, we derive closed-form estimators for the parameters of some probability distributions belonging to the exponential family. A bootstrap bias-reduced version of these proposed closed-form estimators are also derived. A Monte Carlo simulation is performed for the assessment of the estimators. The results are seen to be quite favorable to the proposed bootstrap bias-reduce estimators.