Nonparametric contaminated Gaussian mixture of regressions

TL;DR

This paper introduces a robust semi- and non-parametric mixture of regressions model using contaminated Gaussian distributions, effectively handling outliers while enabling clustering and outlier detection.

Contribution

It proposes a novel contaminated Gaussian mixture of regressions model with algorithms for robust estimation, addressing outlier sensitivity in traditional models.

Findings

Robust models outperform traditional Gaussian mixtures in presence of outliers.

Algorithms successfully perform clustering and outlier detection.

Real data applications demonstrate practical utility.

Abstract

Semi- and non-parametric mixture of regressions are a very useful flexible class of mixture of regressions in which some or all of the parameters are non-parametric functions of the covariates. These models are, however, based on the Gaussian assumption of the component error distributions. Thus, their estimation is sensitive to outliers and heavy-tailed error distributions. In this paper, we propose semi- and non-parametric contaminated Gaussian mixture of regressions to robustly estimate the parametric and/or non-parametric terms of the models in the presence of mild outliers. The virtue of using a contaminated Gaussian error distribution is that we can simultaneously perform model-based clustering of observations and model-based outlier detection. We propose two algorithms, an expectation-maximization (EM)-type algorithm and an expectation-conditional-maximization (ECM)-type algorithm, to perform maximum likelihood and local-likelihood kernel estimation of the parametric and non-parametric of the proposed models, respectively. The robustness of the proposed models is examined using an extensive simulation study. The practical utility of the proposed models is demonstrated using real data.