Robust mixture regression based on the skew t distribution

Mixtura robusta de modelos de regresión basada en la distribución t asimétrica

In this study, we propose a robust mixture regression procedure based on the skew t distribution to model heavy-tailed and/or skewed errors in a mixture regression setting. Using the scale mixture representation of the skew  t distribution, we give an Expectation Maximization (EM) algorithm to compute the maximum likelihood (ML) estimates for the paramaters of interest. The performance of proposed estimators is demonstrated by a simulation study and a real data example.

En este estudio se explora una mixtura robusta de modelos de regresión basada en la distribución t asimétrica, con el propósito de modelar colas pesadas o asimétricas en los errores, en un escenario de mixtura de regresiones. Se usa un algoritmo EM para obtener los estimadores máximo verosímiles empleando una mixtura de escala de la distribución t asimétrica. El comportamiento de los estimadores propuestos se ilustra a través de une estudio de simulación y de un ejemplo con datos reales.

Robust Mixture Regression Based on the Skew t Distribution Mixtura robusta de modelos de regresión basada en la distribución t asimétrica FATMA ZEHRA Doğru¹, OLCAY ARSLAN²

¹Giresun University, Faculty of Arts and Sciences, Department of Statistics, Giresun, Turkey. PhD. Email: fatma.dogru@giresun.edu.tr
²Ankara University, Faculty of Science, Department of Statistics, Ankara, Turkey. PhD. Email: oarslan@ankara.edu.tr

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Abstract

In this study, we explore a robust mixture regression procedure based on the skew t distribution in order to model heavy-tailed and/or skewed errors in a mixture regression setting. We present an EM-type algorithm to compute the maximum likelihood estimators for the parameters of interest using the scale mixture representation of the skew t distribution. The performance of proposed estimators is demonstrated by a simulation study and a real data example.

Key words: EM Algorithm, Maximum Likelihood, Mixture Regression Model, Skew t Distribution.

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Resumen

Palabras clave: Algoritmo EM, máxima verosimilitud, mixtura de regresiones, distribución t asimétrica.

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Texto completo disponible en PDF

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[Recibido en abril de 2015. Aceptado en febrero de 2016]

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Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

@ARTICLE{RCEv40n1a09,
    AUTHOR  = Dogru, Fatma Zehra and Arslan, Olcay},
    TITLE   = {{Robust Mixture Regression Based on the Skew t Distribution}},
    JOURNAL = {Revista Colombiana de Estadística},
    YEAR    = {2017},
    volume  = {40},
    number  = {1},
    pages   = {45-64}
}

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