A0437
Title: A new approach to estimate semi-parametric Gaussian mixtures of regressions with varying mixing proportions
Authors: Sphiwe Skhosana - University of Pretoria (South Africa) [presenting]
Sollie Millard - University of Pretoria (South Africa)
Frans Kanfer - University of Pretoria (South Africa)
Abstract: The semi-parametric Gaussian mixture of regressions with varying proportions (SPGMRVPs) model is a flexible version of a Gaussian mixture of linear regressions (GMLRs) model. The model assumes that the mixing probabilities are non-parametric functions of the covariate(s). Traditional methods of estimation are not guaranteed to produce reliable estimates of the model. A local-likelihood approach for estimating the non-parametric functions requires that we maximize a set of local-likelihood functions. Using the Expectation-Maximization (EM) algorithm to separately maximize each local-likelihood function may lead to label switching. This is because the responsibilities calculated at each local E-step might not be aligned. The consequence of this label-switching is wiggly and non-smooth non-parametric functions as a result of incorrect component identification. We propose a novel approach to address label-switching and obtain improved estimates. We propose a model-based approach to address the label-switching problem. We reformulate the SPGMRVPs model as a mixture of local GMLRs. Estimating the mixture of GMLRs is equivalent to simultaneously maximizing the local-likelihood functions. Next, we propose one-step backfitting estimates of the parametric and non-parametric terms. The effectiveness and practical utility of the proposed approach is demonstrated using Monte Carlo simulations and environmental data analysis.
