Mixtures of nonparametric autoregressions

Abstract

We consider data generating mechanisms which can be represented as mixtures of finitely many regression or autoregression models. We propose nonparametric estimators for the functions characterising the various mixture components based on a local quasi maximum likelihood approach and prove their consistency. We present an EM algorithm for calculating the estimates numerically which is mainly based on iteratively applying common local smoothers and discuss its convergence properties.

Keywords:

• nonparametric regression
• nonparametric autoregression
• mixture
• hidden variables
• EM algorithm
• kernel estimates
• local likelihood

AMS Subject Classification :

• 62G08
• 62M10

Acknowledgements

We thank an anonymous referee for recommendations which led to a considerable improvement of the paper. The work was supported by the Deutsche Forschungsgemeinschaft (DFG) as well as by the Center for Mathematical and Computational Modelling (CM)² funded by the state of Rhineland-Palatinate.