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Title: A one-step backfitting algorithm for estimating the semi-parametric mixture of partial linear models 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 mixture of partial linear models (SPMPLMs) offers flexibility in modelling heterogeneous regression relationships. In addition, it reduces the curse of dimensionality problem. Given a set of covariates, the model assumes that the component regression function (CRF) is a linear combination of a parametric function of some of the covariates and a non-parametric function of the other covariates. In practice, the CRF is usually estimated at a set of grid points using a local profile likelihood approach via the Expectation-Maximization (EM) algorithm. However, maximizing each local-likelihood function separately does not guarantee that the responsibilities obtained at the E-step of the EM algorithm align at each grid point leading to a label-switching problem. This results in non-smooth CRFs. We propose a modified EM algorithm in the form of a one-step backfitting algorithm to account for the label-switching by tracking the roughness of the CRF. Because of the computational intensity of the one-step procedure, we also propose an alternative plug-in estimation procedure. We use simulation and an application on a real-world data set to demonstrate the performance of both algorithms. In our simulation study, the proposed algorithm performs similarly to, if not better than, competitive methods for all the scenarios investigated.