Functional partial linear model

Abstract

When predicting scalar responses in the situation where the explanatory variables are functions, it is sometimes the case that some functional variables are related to responses linearly while other variables have more complicated relationships with the responses. In this paper, we propose a new semi-parametric model to take advantage of both parametric and nonparametric functional modelling. Asymptotic properties of the proposed estimators are established and finite sample behaviour is investigated through a small simulation experiment.

Keywords:

• functional data
• Kernel regression
• partial linear model
• rates of convergence

AMS Subject Classification :

• 62G20
• 62G05

Acknowledgements

The author wants to thank the Associate Editor and two referees for their comments and suggestions that greatly improved the paper. In particular, the convergence rates obtained in this paper are better than those obtained in the original manuscript, thanks to the suggestion of one anonymous referee. He also thanks Professor Ferraty for his clarification on some relevant results on uniform convergence of kernel estimators, through personal communications. The research is supported by Singapore MOE Tier 1 RG 36/09.