Joint modelling of location and scale parameters of the skew-normal distribution

Joint location and scale models of the skew-normal distribution provide useful ex- tension for joint mean and variance models of the normal distribution when the data set under consideration involves asymmetric outcomes. This paper focuses on the maximum likelihood estimation of joint location and scale models of the skew-normal distribution. The proposed procedure can simultaneously estimate parameters in the location model and the scale model. Simulation studies and a real example are used to illustrate the proposed methodologies.

A skew–normal mixture of joint location, scale and skewness models

Normal mixture regression models are one of the most important statistical data analysis tools in a heterogeneous population. When the data set under consideration involves asymmetric outcomes, in the last two decades, the skew normal distribution has been shown beneficial in dealing with asymmetric data in various theoretic and applied problems. In this paper, we propose and study a novel class of models： a skew-normal mixture of joint location, scale and skewness models to analyze the heteroscedastic skew-normal data coming from a heterogeneous population. The issues of maximum likelihood estimation are addressed. In particular, an Expectation-Maximization （EM） algorithm for estimating the model parameters is developed. Properties of the estimators of the regression coefficients are evaluated through Monte Carlo experiments. Results from the analysis of a real data set from the Body Mass Index （BMI） data are presented.

Variable selection for skew-normal mixture of joint location and scale models

Although there are many papers on variable selection methods based on mean model in the nite mixture of regression models,little work has been done on how to select signi cant explanatory variables in the modeling of the variance parameter.In this paper,we propose and study a novel class of models:a skew-normal mixture of joint location and scale models to analyze the heteroscedastic skew-normal data coming from a heterogeneous population.The problem of variable selection for the proposed models is considered.In particular,a modi ed Expectation-Maximization(EM)algorithm for estimating the model parameters is developed.The consistency and the oracle property of the penalized estimators is established.Simulation studies are conducted to investigate the nite sample performance of the proposed methodolo-gies.An example is illustrated by the proposed methodologies.

Variable Selection in Joint Location, Scale and Skewness Models of the Skew-Normal Distribution

Variable selection is an important research topic in modern statistics, traditional variable selection methods can only select the mean model and(or) the variance model, and cannot be used to select the joint mean, variance and skewness models. In this paper, the authors propose the joint location, scale and skewness models when the data set under consideration involves asymmetric outcomes,and consider the problem of variable selection for our proposed models. Based on an efficient unified penalized likelihood method, the consistency and the oracle property of the penalized estimators are established. The authors develop the variable selection procedure for the proposed joint models, which can efficiently simultaneously estimate and select important variables in location model, scale model and skewness model. Simulation studies and body mass index data analysis are presented to illustrate the proposed methods.