Automatic and location-adaptive estimation in functional single-index regression

Abstract

This paper develops a new automatic and location-adaptive procedure for estimating regression in a Functional Single-Index Model (FSIM). This procedure is based on $k$-Nearest Neighbours ($k$NN) ideas. The asymptotic study includes results for automatically data-driven selected number of neighbours, making the procedure directly usable in practice. The local feature of the $k$NN approach insures higher predictive power compared with usual kernel estimates, as illustrated in some finite sample analysis. As by-product we state as preliminary tools some new uniform asymptotic results for kernel estimates in the FSIM model.

31 pages, 5 figures, 4 tables

References in corpus (1)

• Single and multiple index functional regression models with nonparametric link

Cited by in corpus (3)

• Sparse semiparametric regression when predictors are mixture of functional and high-dimensional variables
• A $k$NN procedure in semiparametric functional data analysis
• Fast and efficient algorithms for sparse semiparametric bi-functional regression