A1431
Title: Estimating semiparametric Gaussian mixtures of nonparametric regressions with an application in environmental economics
Authors: Sphiwe Skhosana - University of Pretoria (South Africa) [presenting]
Sollie Millard - University of Pretoria (South Africa)
Frans Kanfer - University of Pretoria (South Africa)
Abstract: Semiparametric mixtures of Gaussian nonparametric regressions (SPGMNRs) are a flexible class of Gaussian mixtures of regression models. These models assume that the component regression functions (CRFs) are nonparametric functions of the covariates, whereas the mixing proportions and variances are constant (parametric). However, local-likelihood estimation of the nonparametric (CRFs) poses a computational challenge. Traditional expectation-maximization (EM) optimisation of the local-likelihood functions is not appropriate due to the label-switching problem. Separately applying the EM algorithm on each local-likelihood function will likely result in non-smooth CRFs. This is because the local responsibilities calculated at the local E-step of each EM are not guaranteed to be aligned. The misalignment in the labels can be prevented by making use of the same (global) responsibilities at each local M-step. Thus, the goal is to obtain these global responsibilities. The aim is to propose a novel two-step approach to address label-switching. In the first step, each local-likelihood function is maximized separately to obtain the local responsibilities. In the second step, based on an appropriate objective function, one set of local responsibilities is chosen from the first step as the global responsibilities. The performance and practical usefulness of the proposed method are evaluated using a simulated dataset and a real dataset from environmental economics.
