On the Robust Nonparametric Regression Estimate in the Single Functional Index Model

Abstract

In this work, we construct and study a family of robust nonparametric estimators for a regression function based on kernel methods. The data are functional, independent and identically distributed, and are linked to a single-index model. Under general conditions, we establish the pointwise and uniform almost complete convergence, as well as the asymptotic normality of the estimator. We explicitly derive the asymptotic variance and, as a result, provide confidence bands for the theoretical parameter. A simulation study is conducted to illustrate the proposed methodology.

Keywords

Asymptotic normality / Functional data / Functional Hilbert space / Kernel estimate / Nonparametric model / Robust regression / Simulation study / Single functional index model / Uniform almost complete convergence / 62G05 / 62G20 / 62H12

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School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature