Existence and Consistency of the Maximum Pseudo \b{eta}-Likelihood Estimators for Multivariate Normal Mixture Models

TL;DR

This paper establishes the existence and weak consistency of a new robust estimator for multivariate normal mixture models, which simplifies computation while maintaining statistical reliability.

Contribution

It rigorously proves the existence and weak consistency of the maximum pseudo ta-likelihood estimator for MVN mixture models under reasonable assumptions.

Findings

Proves the estimator's existence under certain conditions.

Establishes the weak consistency of the estimator.

Provides a computationally simpler alternative to existing methods.

Abstract

Robust estimation under multivariate normal (MVN) mixture model is always a computational challenge. A recently proposed maximum pseudo \b{eta}-likelihood estimator aims to estimate the unknown parameters of a MVN mixture model in the spirit of minimum density power divergence (DPD) methodology but with a relatively simpler and tractable computational algorithm even for larger dimensions. In this letter, we will rigorously derive the existence and weak consistency of the maximum pseudo \b{eta}-likelihood estimator in case of MVN mixture models under a reasonable set of assumptions.