Local Weighted Average Estimation of the Regression Operator for Functional Data

Abstract

We are concerned with the problem of local weighted average estimation of the regression operator when the responses are real-valued random variables, the explanatory data are of functional fixed-design type, and the errors consist of an independent and identically distributed variables. In this article, our main contributions on the local linear functional estimation concern from one part, the situation when the data are of functional fixed-design kind, and from the other part, in deriving uniform asymptotic results on the behavior of this estimator with respect to the topological properties of the space data (normed or semi-metric).

Keywords:

• Functional fixed-design data
• Local polynomial fitting
• Nonparametric model
• Quadratic error
• Small ball frequencies
• Small ball probabilities

Mathematics Subject Classification:

• Primary 62G05
• Secondary 62G07, 62G08, 62G35, 62G20

Acknowledgments

The authors wish to express their gratitude to the Associate Editor and an anonymous referee for their helpful comments allowing to which helped to greatly improve an earlier version of this work.