B1660
Title: A new approach to estimate semi-parametric Gaussian mixtures of non-parametric regressions
Authors: Sphiwe Skhosana - University of Pretoria (South Africa) [presenting]
Sollie Millard - University of Pretoria (South Africa)
Frans Kanfer - University of Pretoria (South Africa)
Abstract: Semi-parametric Gaussian mixtures of non-parametric regressions (SPGMNRs) are a flexible extension of Gaussian mixtures of linear regressions. These models assume that the component regression functions (CRFs) are non-parametric functions of the covariates whereas the component mixing proportions and variances are parametric. Unfortunately, likelihood estimation of the non-parametric functions poses a challenge. The latter requires that a set of local likelihood functions is maximized. Using the expectation-maximization (EM) algorithm to separately maximize each local-likelihood function may lead to label-switching. This is because the posterior probabilities calculated at each local E-step are not guaranteed to be aligned. The consequence of label-switching is wiggly and non-smooth CRFs. A unified approach is proposed to address label switching and automatically select the number and location of the points. The SPGMNRs model is first reformulated as a mixture of Gaussian mixture models (GMMs). The resulting model is estimated using a modified expectation-conditional-maximization (ECM) algorithm. The mixing weights of the GMMs are used to automatically choose the GMMs to be included in the mixture. Finally, one-step backfitting estimates of the parametric and non-parametric terms are proposed. The effectiveness of the proposed approach is demonstrated using simulations and an application on real data.
