Local linear regression for functional predictor and scalar response

Authors:
Amparo Baíllo;Aurea Grané
Affiliations:
Departamento de Análisis Económico: Economía Cuantitativa, Universidad Autónoma de Madrid, 28049 Madrid, Spain;Departamento de Estadística, Universidad Carlos III de Madrid, C/ Madrid 126, 28903 Getafe Madrid, Spain
Venue:
Journal of Multivariate Analysis
Year:
2009

Citing 3
Cited 3

Estimation in generalized linear models for functional data via penalized likelihood

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Nonparametric Functional Data Analysis: Theory and Practice (Springer Series in Statistics)

Nonparametric Functional Data Analysis: Theory and Practice (Springer Series in Statistics)
Robust estimation and classification for functional data via projection-based depth notions

Computational Statistics

Distance-based local linear regression for functional predictors

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Functional contour regression

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Theoretical and practical aspects of the quadratic error in the local linear estimation of the conditional density for functional data

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Abstract

The aim of this work is to introduce a new nonparametric regression technique in the context of functional covariate and scalar response. We propose a local linear regression estimator and study its asymptotic behaviour. Its finite-sample performance is compared with a Nadayara-Watson type kernel regression estimator and with the linear regression estimator via a Monte Carlo study and the analysis of two real data sets. In all the scenarios considered, the local linear regression estimator performs better than the kernel one, in the sense that the mean squared prediction error is lower.