Abstract
In this paper, we propose a robust mixture regression model based on the skew scale mixtures of normal distributions (RMR-SSMN) which can accommodate asymmetric, heavy-tailed and contaminated data better. For the variable selection problem, the penalized likelihood approach with a new combined penalty function which balances the SCAD and l2 penalty is proposed. The adjusted EM algorithm is presented to get parameter estimates of RMR-SSMN models at a faster convergence rate. As simulations show, our mixture models are more robust than general FMR models and the new combined penalty function outperforms SCAD for variable selection. Finally, the proposed methodology and algorithm are applied to a real data set and achieve reasonable results.
Highlights
We propose a robust mixture regression model based on the skew scale mixtures of normal distributions (RMR-Skew Scale Mixtures of Normal (SSMN)) which can accommodate asymmetric, heavy-tailed and contaminated data better
We mainly propose a robust mixture regression model based on the skew scale mixtures of normal distributions (RMR-SSMN) which can avoid the potential limitation of normal mixtures
A new penalty function (MIXL2SCAD) which combines SCAD and l2 penalties is presented for variable selection
Summary
The arc-sine laws for the Wiener process and the skew Brownian motion [1] are widely used in finance if the market is homogeneous. It is well known that using the normal distribution to model data with asymmetric and heavy-tailed behaviors is unsuitable, and the parameter estimates are sensitive to outliers. The problem of variable selection in FMR models has been widely discussed recently. We utilize the SCAD and a new penalty function proposed in this paper which balance the SCAD and l2 penalty to perform variable selection on a robust mixture regression model based on Skew Scale Mixtures of Normal (SSMN) distributions [9] and this robust model can accommodate asymmetric and heavy-tailed data better.
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