Consistency, breakdown robustness, and algorithms for robust improper maximum likelihood clustering
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 multivariate 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.
Cite
@article{arxiv.1309.6895,
title = {Consistency, breakdown robustness, and algorithms for robust improper maximum likelihood clustering},
author = {Pietro Coretto and Christian Hennig},
journal= {arXiv preprint arXiv:1309.6895},
year = {2018}
}
Comments
The title of this paper was originally: "A consistent and breakdown robust model-based clustering method"