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Testing separability of space-time functional processes

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  • P. Constantinou
  • P. Kokoszka
  • M. Reimherr

Abstract

SummarySeparability is a common simplifying assumption on the covariance structure of spatiotemporal functional data. We present three tests of separability, one a functional extension of the Monte Carlo likelihood method of Mitchell et al. (2006) and two based on quadratic forms. Our tests are based on asymptotic distributions of maximum likelihood estimators and do not require Monte Carlo simulation. The main theoretical contribution of this paper is the specification of the joint asymptotic distribution of these estimators, which can be used to derive many other tests. The main methodological finding is that one of the quadratic form methods, which we call a norm approach, emerges as a clear winner in terms of finite-sample performance in nearly every setting we considered. This approach focuses directly on the Frobenius distance between the spatiotemporal covariance function and its separable approximation. We demonstrate the efficacy of our methods via simulations and application to Irish wind data.

Suggested Citation

  • P. Constantinou & P. Kokoszka & M. Reimherr, 2017. "Testing separability of space-time functional processes," Biometrika, Biometrika Trust, vol. 104(2), pages 425-437.
  • Handle: RePEc:oup:biomet:v:104:y:2017:i:2:p:425-437.
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    File URL: http://hdl.handle.net/10.1093/biomet/asx013
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    Cited by:

    1. Davide Pigoli & Pantelis Z. Hadjipantelis & John S. Coleman & John A. D. Aston, 2018. "The statistical analysis of acoustic phonetic data: exploring differences between spoken Romance languages," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 67(5), pages 1103-1145, November.
    2. T Masak & S Sarkar & V M Panaretos, 2023. "Separable expansions for covariance estimation via the partial inner product," Biometrika, Biometrika Trust, vol. 110(1), pages 225-247.
    3. Chen, Yichao & Pun, Chi Seng, 2019. "A bootstrap-based KPSS test for functional time series," Journal of Multivariate Analysis, Elsevier, vol. 174(C).
    4. Dennis Schroers, 2024. "Robust Functional Data Analysis for Stochastic Evolution Equations in Infinite Dimensions," Papers 2401.16286, arXiv.org, revised Jun 2024.
    5. Chen, Xin & Yang, Dan & Xu, Yan & Xia, Yin & Wang, Dong & Shen, Haipeng, 2023. "Testing and support recovery of correlation structures for matrix-valued observations with an application to stock market data," Journal of Econometrics, Elsevier, vol. 232(2), pages 544-564.
    6. David M Alexander & Tonio Ball & Andreas Schulze-Bonhage & Cees van Leeuwen, 2019. "Large-scale cortical travelling waves predict localized future cortical signals," PLOS Computational Biology, Public Library of Science, vol. 15(11), pages 1-34, November.

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