Simultaneous confidence bands for nonparametric regression with functional data

2009/08/13 by David A. Degras, Degras, David A. · 1 citation
Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistics Theory (math.ST) #math.ST #stat.ME #stat.TH

paper · pdf · doi:10.48550/arxiv.0908.1980

Accepted at Statistica Sinica (SS-09-207)

arxiv created 2010/07/20 · arxiv updated 2015/03/13

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.

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