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A generalized class of skew distributions and associated robust quantile regression models
Author(s) -
Wichitaksorn Nuttanan,
Choy S. T. Boris,
Gerlach Richard
Publication year - 2014
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.1002/cjs.11228
Subject(s) - skewness , mathematics , statistics , quantile regression , skew , univariate , econometrics , parametric statistics , quantile , markov chain monte carlo , regression analysis , skew normal distribution , monte carlo method , multivariate statistics , computer science , telecommunications
This article proposes a generalized class of univariate skew distributions that are constructed through partitioning two scaled mixture of normal (Gaussian) distributions. The proposed distributions have a skewness parameter defined in the interval (0,1), allowing direct application to parametric quantile regression. Employing scale mixture of normals facilitates efficient estimation via Markov chain Monte Carlo methods. Two simulation studies, one on estimation with skew error regression models, the other on parametric quantile regression models reveal favourable estimation properties. Two corresponding empirical studies, one analysing U.S. market returns, the other on infant birthweight data further illustrate the proposed distributions and their estimation. The Canadian Journal of Statistics 42: 579–596; 2014 © 2014 Statistical Society of Canada