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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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    References listed on IDEAS

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    Cited by:

    1. Clémençon, Stephan & Huet, Nathan & Sabourin, Anne, 2024. "Regular variation in Hilbert spaces and principal component analysis for functional extremes," Stochastic Processes and their Applications, Elsevier, vol. 174(C).

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