Existence and Consistency of the Maximum Pseudo e̱ṯa̱-Likelihood Estimators for Multivariate Normal Mixture Models

05/11/2022

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by   Soumya Chakraborty, et al.

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Robust estimation under multivariate normal (MVN) mixture model is always a computational challenge. A recently proposed maximum pseudo e̱ṯa̱-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 e̱ṯa̱-likelihood estimator in case of MVN mixture models under a reasonable set of assumptions.