A monotonic MM-type algorithm for estimation of nonparametric finite mixture models with dependent marginals

TL;DR

This paper introduces a new monotonic MM algorithm for estimating components of nonparametric finite mixture models with dependent marginals, ensuring convergence and comparable performance to existing methods.

Contribution

It presents the first monotonic MM algorithm for nonparametric mixture models with dependent marginals, improving convergence guarantees over previous approaches.

Findings

Algorithm converges to a local maximum of the penalized likelihood.

Performance is comparable to existing non-monotonic algorithms.

Demonstrated effectiveness on simulated and real datasets.

Abstract

In this manuscript, we consider a finite nonparametric mixture model with non-independent marginal density functions. Dependence between the marginal densities is modeled using a copula device. Until recently, no deterministic algorithms capable of estimating components of such a model have been available. A deterministic algorithm that is capable of this has been proposed in \citet*{levine2024smoothed}. That algorithm seeks to maximize a smoothed nonparametric penalized log-likelihood; it seems to perform well in practice but does not possess the monotonicity property. In this manuscript, we introduce a deterministic MM (Minorization-Maximization) algorithm for estimation of components of this model that is also maximizing a smoothed penalized nonparametric log-likelihood but that is monotonic with respect to this objective functional. Besides the convergence of the objective functional, the convergence of a subsequence of arguments of this functional, generated by this algorithm, is also established. The behavior of this algorithm is illustrated using both simulated datasets as well as a real dataset. The results illustrate performance that is at least comparable to the earlier algorithm of \citet*{levine2024smoothed}. A discussion of the results and possible future research directions make up the last part of the manuscript.