Simultaneous confidence bands for nonparametric regression with
functional data
D. Degras. (2009)cite arxiv:0908.1980Comment: Accepted at Statistica Sinica (SS-09-207).
Abstract
We consider nonparametric regression in the context of functional data, that
is, when a random sample of functions is observed on a fine grid. We obtain a
functional asymptotic normality result allowing to build simultaneous
confidence bands (SCB) for various estimation and inference tasks. Two
applications to a SCB procedure for the regression function and to a
goodness-of-fit test for curvilinear regression models are proposed. The first
one has improved accuracy upon the other available methods while the second can
detect local departures from a parametric shape, as opposed to the usual
goodness-of-fit tests which only track global departures. A numerical study of
the SCB procedures and an illustration with a speech data set are provided.
Description
[0908.1980] Simultaneous confidence bands for nonparametric regression with functional data
%0 Journal Article
%1 degras2009simultaneous
%A Degras, David A.
%D 2009
%K non-parametric readings regression uncertainty
%T Simultaneous confidence bands for nonparametric regression with
functional data
%U http://arxiv.org/abs/0908.1980
%X We consider nonparametric regression in the context of functional data, that
is, when a random sample of functions is observed on a fine grid. We obtain a
functional asymptotic normality result allowing to build simultaneous
confidence bands (SCB) for various estimation and inference tasks. Two
applications to a SCB procedure for the regression function and to a
goodness-of-fit test for curvilinear regression models are proposed. The first
one has improved accuracy upon the other available methods while the second can
detect local departures from a parametric shape, as opposed to the usual
goodness-of-fit tests which only track global departures. A numerical study of
the SCB procedures and an illustration with a speech data set are provided.
@article{degras2009simultaneous,
abstract = {We consider nonparametric regression in the context of functional data, that
is, when a random sample of functions is observed on a fine grid. We obtain a
functional asymptotic normality result allowing to build simultaneous
confidence bands (SCB) for various estimation and inference tasks. Two
applications to a SCB procedure for the regression function and to a
goodness-of-fit test for curvilinear regression models are proposed. The first
one has improved accuracy upon the other available methods while the second can
detect local departures from a parametric shape, as opposed to the usual
goodness-of-fit tests which only track global departures. A numerical study of
the SCB procedures and an illustration with a speech data set are provided.},
added-at = {2019-11-04T11:26:14.000+0100},
author = {Degras, David A.},
biburl = {https://www.bibsonomy.org/bibtex/26fa1777606a0dbfb05649fe1738994b9/kirk86},
description = {[0908.1980] Simultaneous confidence bands for nonparametric regression with functional data},
interhash = {62dcafd9f388d2b8df5253e49206f6ca},
intrahash = {6fa1777606a0dbfb05649fe1738994b9},
keywords = {non-parametric readings regression uncertainty},
note = {cite arxiv:0908.1980Comment: Accepted at Statistica Sinica (SS-09-207)},
timestamp = {2019-11-04T11:31:36.000+0100},
title = {Simultaneous confidence bands for nonparametric regression with
functional data},
url = {http://arxiv.org/abs/0908.1980},
year = 2009
}