Diagnostics on nonlinear model with scale mixtures of skew-normal and first-order autoregressive errors

Abstract

In this work, we develop some diagnostics for nonlinear regression model with scale mixtures of skew-normal (SMSN) and first-order autoregressive errors. The SMSN distribution class covers symmetric as well as asymmetric and heavy-tailed distributions, which offers a more flexible framework for modelling. Maximum-likelihood (ML) estimates are computed via an expectation–maximization-type algorithm. Local influence diagnostics and score test for the correlation are also derived. The performances of the ML estimates and the test statistic are investigated through Monte Carlo simulations. Finally, a real data set is used to illustrate our diagnostic methods.

Keywords:

• AR(1) errors
• diagnostics
• local influence
• nonlinear models
• scale mixtures of skew-normal distributions
• score test

Acknowledgements

This research was supported by the Natural Science Foundation of Jiangsu Province of China (Grant No. BK2012459), and the National Science Foundation of China (Grant No. 11171065). We are very grateful to the editor and reviewers for their helpful comments and suggestions which greatly improve our work.