Inference and diagnostics for heteroscedastic nonlinear regression models under skew scale mixtures of normal distributions

Abstract

The heteroscedastic nonlinear regression model (HNLM) is an important tool in data modeling. In this paper we propose a HNLM considering skew scale mixtures of normal (SSMN) distributions, which allows fitting asymmetric and heavy-tailed data simultaneously. Maximum likelihood (ML) estimation is performed via the expectation-maximization (EM) algorithm. The observed information matrix is derived analytically to account for standard errors. In addition, diagnostic analysis is developed using case-deletion measures and the local influence approach. A simulation study is developed to verify the empirical distribution of the likelihood ratio statistic, the power of the homogeneity of variances test and a study for misspecification of the structure function. The method proposed is also illustrated by analyzing a real dataset.