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Interval and band estimation for curves with jumps

Part of: Nonparametric inference

Published online by Cambridge University Press:  14 July 2016

Irène Gijbels ,
Peter Hall  and
Aloïs Kneip
Irène Gijbels
Affiliation:
Institut de Statistique, Université Catholique de Louvain, 20 Voie du Roman Pays, B-1348 Louvain-la-Neuve, Belgium. Email address: gijbels@stat.ucl.ac.be
Peter Hall
Affiliation:
Centre for Mathematics and Its Applications, Mathematical Sciences Institute, Australian National University, Canberra, ACT 0200, Australia. Email address: peter.hall@anu.edu.au
Aloïs Kneip
Affiliation:
Johannes Gutenberg Universität-Mainz, Lehrstuhl für Statistik und Mathematik FB, Rechts-und Witschaftswissenschaften, Jakob-Welder-Weg 9, D-55128 Mainz, Germany. Email address: kneip@wiwi.uni-mainz.de
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Abstract

Jump points in curves arise when the conditions under which data are generated change suddenly, for example because of an unplanned change in a treatment. This paper suggests bootstrap methods for quantifying the error in estimates of jump points, and for constructing confidence intervals for jump points and confidence bands for the curve. These problems have the unusual feature that the sampling error of the jump-point estimator often has a highly non-normal distribution, which depends intimately on the distribution of regression errors. The methods are illustrated by a simulation study as well as by an application to data on the annual flow volume of the Nile river.

Keywords

Bandwidthbootstrapchange pointconfidence intervalcurve estimationdiscontinuitykernel methodsnonparametric regression

MSC classification

Primary: 62G15: Tolerance and confidence regions
Secondary: 62G09: Resampling methods
Type
Part 2. Estimation methods
Information
Journal of Applied Probability , Volume 41 , Issue A: Stochastic Methods and their Applications , 2004 , pp. 65 - 79
Copyright
Copyright © Applied Probability Trust 2004 

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