Semiparametric regression models under skew scale mixtures of normal distributions

Abstract

Semiparametric models (SM) are an important tool in modeling environmental data where generally a covariate presents an unknown nonlinear behavior. Usually, the error component is assumed to follow a normal distribution. However, in some situations, the response variable is skewed and heavy-tailed. This paper aims to extend the SMs allowing the errors to follow a skew scale mixture of normal distributions, increasing the model's flexibility. In particular, we develop the EM algorithm for the proposed model, diagnostic analysis via global, local influence, and generalized leverage. A simulation study is also conducted to evaluate the efficiency of the EM algorithm. Finally, a suitable transformation is applied in a data set on ragweed pollen concentration to illustrate the utility of the proposed model.