Heteroscedastic partially linear model under skew-normal distribution with application in ragweed pollen concentration

Abstract

We introduce a new class of heteroscedastic partially linear model (PLM) with skew-normal distribution. Maximum likelihood estimation of the model parameters by the ECM algorithm (Expectation/Conditional Maximization) as well as influence diagnostics for the new model are investigated. In addition, a Likelihood Ratio test for assessing the homogeneity of the scale parameter is presented. Simulation studies for assessing the performance of the ECM algorithm and the Likelihood Ratio test statistics for homogeneity of variance are developed. Also, a study for misspecification of the structure function is considered. Finally, an application of the new heteroscedastic PLM to a real data set on ragweed pollen concentration is presented to show that it provides a better fit than the classic homocedastic PLM. We hope that the proposed model may attract applications in different areas of knowledge.

Keywords:

• Partially linear models
• skew-normal distribution
• heteroscedasticity
• ECM algorithm
• local influence

Acknowledgments

We thank the Associate Editor and referees for their helpful comments and suggestions, leading to the improvement of the paper.

Disclosure statement

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

Notes

1 http://azzalini.stat.unipd.it/SN/index.html

Additional information

Funding

This work was supported by CNPq and Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG).