An EM Gradient Algorithm for Mixture Models with Components Derived from the Manly Transformation

TL;DR

This paper introduces an EM gradient algorithm for mixture models with components based on the Manly transformation, offering an alternative to Nelder-Mead optimization in the M-step, especially effective with good initial estimates.

Contribution

It proposes a new EM gradient algorithm using Newton's method for updating skew parameters in Manly transformation-based mixture models, improving upon existing optimization methods.

Findings

The EM gradient algorithm performs well with good initial estimates.

It provides an efficient alternative to Nelder-Mead optimization.

The method enhances parameter estimation in Manly transformation mixture models.

Abstract

Zhu and Melnykov (2018) develop a model to fit mixture models when the components are derived from the Manly transformation. Their EM algorithm utilizes Nelder-Mead optimization in the M-step to update the skew parameter, $\boldsymbol{\lambda}_g$. An alternative EM gradient algorithm is proposed, using one step of Newton's method, when initial estimates for the model parameters are good.