Estimation of Dirichlet distribution parameters with bias-reducing adjusted score functions

TL;DR

This paper introduces bias-reducing adjusted score functions for estimating Dirichlet distribution parameters, improving accuracy especially in small samples, and compares these methods with traditional maximum likelihood estimation through simulations and real data.

Contribution

It proposes novel bias-reducing score functions for Dirichlet parameter estimation, enhancing estimation accuracy over maximum likelihood in small samples.

Findings

Bias reduction improves estimation accuracy.

Adjusted score methods outperform maximum likelihood in simulations.

Application demonstrates practical effectiveness.

Abstract

The Dirichlet distribution, also known as multivariate beta, is the most used to analyse frequencies or proportions data. Maximum likelihood is widespread for estimation of Dirichlet's parameters. However, for small sample sizes, the maximum likelihood estimator may shows a significant bias. In this paper, Dirchlet's parameters estimation is obtained through modified score functions aiming at mean and median bias reduction of the maximum likelihood estimator, respectively. A simulation study and an application compare the adjusted score approaches with maximum likelihood.