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.

Keywords:

• ECME-algorithm
• Semiparametric regression models
• Skew scale mixtures of normal distributions

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This study was supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico; Fundação de Amparo à Pesquisa do Estado de Minas Gerais.