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Article . 2010
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Article . 2010
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On the Validity of the Bootstrap in Non-Parametric Functional Regression

On the validity of the bootstrap in non-parametric functional regression
Authors: Ferraty, Frédéric; van Keilegom, Ingrid; Vieu, Philippe;

On the Validity of the Bootstrap in Non-Parametric Functional Regression

Abstract

The functional nonparametric regression model \(Y=r(\chi)+\varepsilon\) is considered with a functional covariate \(\chi\) and a scalar response \(Y\). A kernel estimate \(\hat r\) is proposed for the regression operator \(r\). A bootstrap methodology is proposed allowing the construction of pointwise confidence intervals for \(r\). It is based on the residuals of \(\hat r\). Asymptotic consistency of the naive and wild bootstrap is demonstrated. Bandwidth selection for \(\hat r\) is discussed, and results of simulations are presented.

Countries
Belgium, France
Keywords

62G08 (62G09), wild bootstrap, kernel regression estimates, nonparametric regression, kernel estimator, naive bootstrap, Computational problems in statistics, Asymptotic normality, Nonparametric statistical resampling methods, Nonparametric regression and quantile regression, functional data, confidence intervals, bandwidth selection

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
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