有限混合回归(FMR)模型中的变量选择经常用于统计建模中。FMR模型中变量选择的大多数应用都使用正态分布进行回归误差。这样的假设不适合于包含具有不对称行为的一组或多组观察的一组数据。在本文中,我们介绍了使用偏正态分布的FMR模型的变量选择过程。通过适当选择调谐参数,我们建立了我们程序的理论性质,包括变量选择的一致性和估计中的oracle属性。要估计模型的参数,开发了一种用于数值计算的改进的EM算法。通过数值实验和实际数据示例说明了该方法。
Variable selection in finite mixture of regression (FMR) models is frequently used in statistical modeling. The majority of applications of variable selection in FMR models use a normal distribution for regression error. Such assumptions are unsuitable for a set of data containing a group or groups of observations with asymmetric behavior. In this paper, we introduce a variable selection procedure for FMR models using the skew-normal distribution. With appropriate choice of the tuning parameters, we establish the theoretical properties of our procedure, including consistency in variable selection and the oracle property in estimation. To estimate the parameters of the model, a modified EM algorithm for numerical computations is developed. The methodology is illustrated through numerical experiments and a real data example.