Estimation and Application of Skew-normal Data for Generalized Linear Regression

Generalized linear models are generally applied in statistical researches. Since a lot of real data reveal nonnormality especially skew-normality, new assumption is proposed that error terms follow skew-normal distribution to increase the adaptability of GLMs, which forms GLMSNs. To estimate the parameters in the linear part in models, penalized expectation maximization algorithm is extended. This paper focuses on the combination of skew-normal data and GLMs to get more robust results. Several applications and empirical analyses are given to fit GLMSNs and models selection is presented by Bayesian information criterion.