The robust improper maximum likelihood estimator (RIMLE) is a new method for robust multivariate clustering finding approximately Gaussian clusters. It maximizes a pseudo-likelihood defined by adding a component with improper constant density for accommodating outliers to a Gaussian mixture. A special case of the RIMLE is MLE for multi-variate finite Gaussian mixture models. In this paper we treat existence, consistency, and breakdown theory for the RIMLE comprehensively. RIMLE's existence is proved under non-smooth covariance matrix constraints. It is shown that these can be implemented via a computationally feasible Expectation-Conditional Maximization algorithm.

Consistency, Breakdown Robustness, and Algorithms for Robust Improper Maximum Likelihood Clustering

Pietro Coretto
;
2017

Abstract

The robust improper maximum likelihood estimator (RIMLE) is a new method for robust multivariate clustering finding approximately Gaussian clusters. It maximizes a pseudo-likelihood defined by adding a component with improper constant density for accommodating outliers to a Gaussian mixture. A special case of the RIMLE is MLE for multi-variate finite Gaussian mixture models. In this paper we treat existence, consistency, and breakdown theory for the RIMLE comprehensively. RIMLE's existence is proved under non-smooth covariance matrix constraints. It is shown that these can be implemented via a computationally feasible Expectation-Conditional Maximization algorithm.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11386/4702207
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