Finite mixture of regression models

Abstract

This dissertation consists of three articles, proposing extensions of finite mixtures in regression models. Here we consider a flexible class of both univariate and multivariate distributions, which allow adequate modeling of asymmetric data that have multimodality, heavy tails and outlying observations. This class has special cases such as skew-normal, skew-t, skew-slash and skew normal contaminated distributions, as well as symmetric cases. Initially, a model is proposed based on the assumption that the errors follow a finite mixture of scale mixture of skew-normal (FM-SMSN) distribution rather than the conventional normal distribution. Next, we have a censored regression model where we consider that the error follows a finite mixture of scale mixture of normal (SMN) distribution. Next, we propose a censored regression model where we consider that the error follows a finite mixture of scale mixture of normal (SMN) distribution. Finally, we consider a finite mixture of multivariate regression where the error has a multivariate SMSN distribution. For all proposed models, two R packages were developed, which are reported in the appendix.

Sparse Estimation in Finite Mixture of Accelerated Failure Time and Mixture of Regression Models with R Package fmrs

“…The CAMAN package [28] focuses on the analysis of finite semiparametric mixtures. The CensMix package [27] employs parameter estimation in censored linear regression models, where random errors follow a finite mixture of Normal or Student-t distributions.…”