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Extremal dependence measure for functional data

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  • Kim, Mihyun
  • Kokoszka, Piotr

Abstract

Principal component analysis is one of the most fundamental tools of functional data analysis. It leads to an efficient representation of infinitely dimensional objects, like curves, by means of multivariate vectors of scores. We study the dependence between extremal values of the scores using the extremal dependence measure (EDM). The EDM has been proposed and studied for positive bivariate observations. After extending it to multivariate observations, we focus on its application to the vectors of scores of functional data. Estimated scores form a triangular array of dependent random variables. We derive condition guaranteeing that a suitable estimator of the EDM based on these scores converges to the population EDM and is asymptotically normal. These conditions are completely different from those encountered in the second-order theory of functional data. They are formulated within the framework of functional regular variation. Large sample theory is complemented by an application to intraday return curves for certain stocks and by a simulation study.

Suggested Citation

  • Kim, Mihyun & Kokoszka, Piotr, 2022. "Extremal dependence measure for functional data," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    • Handle: RePEc:eee:jmvana:v:189:y:2022:i:c:s0047259x21001652
    DOI: 10.1016/j.jmva.2021.104887
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    1. R de Fondeville & A C Davison, 2018. "High-dimensional peaks-over-threshold inference," Biometrika, Biometrika Trust, vol. 105(3), pages 575-592.
    2. Anthony W. Ledford & Jonathan A. Tawn, 1997. "Modelling Dependence within Joint Tail Regions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(2), pages 475-499.
    3. Davis, Richard & Resnick, Sidney, 1985. "More limit theory for the sample correlation function of moving averages," Stochastic Processes and their Applications, Elsevier, vol. 20(2), pages 257-279, September.
    4. Marc G. Genton & Simone A. Padoan & Huiyan Sang, 2015. "Multivariate max-stable spatial processes," Biometrika, Biometrika Trust, vol. 102(1), pages 215-230.
    5. Anthony W. Ledford & Jonathan A. Tawn, 2003. "Diagnostics for dependence within time series extremes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 521-543, May.
    6. Aneiros, Germán & Cao, Ricardo & Fraiman, Ricardo & Genest, Christian & Vieu, Philippe, 2019. "Recent advances in functional data analysis and high-dimensional statistics," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 3-9.
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