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A Darling–Erdős-type CUSUM-procedure for functional data

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Abstract

The focus of the paper is nonparametric detection of changes in the mean of \(m\)-dependent stationary functional data via a cumulative sum (CUSUM) procedure. We consider a projection-based quasi-maximum likelihood CUSUM-procedure which relies on a Darling–Erdős-type limit theorem. Under mild moment assumptions we investigate the asymptotic properties under the null hypothesis and show consistency under the alternatives of either an abrupt or a gradual change in the mean. The finite sample behavior is illustrated in a small simulation study including an application to temperature data from Hohenpeißenberg (Bavaria, Germany).

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Acknowledgments

We would like to thank the referees for thorough reviews, corrections and valuable suggestions. We acknowledge the data providers in the ECA&D project. Klein Tank, A. M. G. and Coauthors, 2002. Daily dataset of twentieth-century surface air temperature and precipitation series for the European Climate Assessment. Int. J. of Climatol., 22, 1441–1453. Data and metadata available at http://www.ecad.eu.

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  1. Mathematical Institute, University of Cologne, Weyertal 86-90, 50931 , Cologne, Germany

    Leonid Torgovitski

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  1. Leonid Torgovitski
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Correspondence to Leonid Torgovitski.

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Torgovitski, L. A Darling–Erdős-type CUSUM-procedure for functional data. Metrika 78, 1–27 (2015). https://doi.org/10.1007/s00184-014-0487-7

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  • DOI: https://doi.org/10.1007/s00184-014-0487-7

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