Semiparametric mixture of additive regression models

ABSTRACT

In this article, we propose a semiparametric mixture of additive regression models, in which the regression functions are additive and non parametric while the mixing proportions and variances are constant. Compared with the mixture of linear regression models, the proposed methodology is more flexible in modeling the non linear relationship between the response and covariate. A two-step procedure based on the spline-backfitted kernel method is derived for computation. Moreover, we establish the asymptotic normality of the resultant estimators and examine their good performance through a numerical example.

KEYWORDS:

• Additive models
• EM algorithm
• Finite mixture models
• Non parametric regression

MATHEMATICS SUBJECT CLASSIFICATION:

• 62G08

Acknowledgments

The authors are indebted to two referees, whose valuable comments and suggestions led to a much improved presentation.

Funding

Zheng’s research is supported by Graduate Innovation Foundation of Shanghai University of Finance and Economics, grant CXJJ-2014-461.