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An independence test for functional variables based on kernel normalized cross-covariance operator

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  • Manfoumbi Djonguet, Terence Kevin
  • Nkiet, Guy Martial

Abstract

We propose an independence test for random variables valued into metric spaces by using a test statistic obtained from appropriately centering and rescaling the squared Hilbert–Schmidt norm of the usual empirical estimator of normalized cross-covariance operator. We then get asymptotic normality of this statistic under independence hypothesis, so leading to a new test for independence of functional random variables. A simulation study that allows to compare the proposed test to existing ones is provided.

Suggested Citation

  • Manfoumbi Djonguet, Terence Kevin & Nkiet, Guy Martial, 2024. "An independence test for functional variables based on kernel normalized cross-covariance operator," Journal of Multivariate Analysis, Elsevier, vol. 202(C).
    • Handle: RePEc:eee:jmvana:v:202:y:2024:i:c:s0047259x23001392
    DOI: 10.1016/j.jmva.2023.105293
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    References listed on IDEAS

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    1. Aghoukeng Jiofack, Jean Gérard & Nkiet, Guy Martial, 2010. "Testing for lack of dependence between functional variables," Statistics & Probability Letters, Elsevier, vol. 80(15-16), pages 1210-1217, August.
    2. Meintanis, Simos G. & Hušková, Marie & Hlávka, Zdeněk, 2022. "Fourier-type tests of mutual independence between functional time series," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    3. Mirosław Krzyśko & Tomasz Górecki & Waldemar Wołyński & Waldemar Ratajczak, 2016. "An Extension of the Classical Distance Correlation Coefficient for Multivariate Functional Data with Applications," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 17(3), pages 449-466, September.
    4. Horváth, Lajos & Rice, Gregory, 2015. "Testing for independence between functional time series," Journal of Econometrics, Elsevier, vol. 189(2), pages 371-382.
    5. 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.
    6. Lai, Tingyu & Zhang, Zhongzhan & Wang, Yafei & Kong, Linglong, 2021. "Testing independence of functional variables by angle covariance," Journal of Multivariate Analysis, Elsevier, vol. 182(C).
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