Estimation of a change-point in the mean function of functional data

Authors:
Alexander Aue;Robertas Gabrys;Lajos Horváth;Piotr Kokoszka
Affiliations:
Department of Statistics, University of California, Davis, One Shields Avenue, Davis, CA 95616, USA;Department of Mathematics and Statistics, Utah State University, 3900 Old Main Hill, Logan, UT 84322-3900 USA;Department of Mathematics, University of Utah, 155 South 1440 East, Salt Lake City, UT 84112-0090, USA;Department of Mathematics and Statistics, Utah State University, 3900 Old Main Hill, Logan, UT 84322-3900 USA
Venue:
Journal of Multivariate Analysis
Year:
2009

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Abstract

The paper develops a comprehensive asymptotic theory for the estimation of a change-point in the mean function of functional observations. We consider both the case of a constant change size, and the case of a change whose size approaches zero, as the sample size tends to infinity. We show how the limit distribution of a suitably defined change-point estimator depends on the size and location of the change. The theoretical insights are confirmed by a simulation study which illustrates the behavior of the estimator in finite samples.