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Tests for equality of several covariance matrix functions for multivariate functional data

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  • Qiu, Zhiping
  • Fan, Jiangyuan
  • Zhang, Jin-Ting
  • Chen, Jianwei

Abstract

Multivariate functional data are often observed in many scientific fields. This paper considers a multi-sample equal-covariance matrix function testing problem for multivariate functional data. Two new tests are proposed and studied. The asymptotic properties of the two tests under the null hypothesis and a local alternative are investigated. Two methods for approximating the null distributions of the test statistics are described. It is shown that the two tests are root-n consistent. Two simulation studies are conducted to evaluate the finite sample performance of the proposed tests. Finally, the two tests are illustrated via applications to three real multivariate functional data sets.

Suggested Citation

  • Qiu, Zhiping & Fan, Jiangyuan & Zhang, Jin-Ting & Chen, Jianwei, 2024. "Tests for equality of several covariance matrix functions for multivariate functional data," Journal of Multivariate Analysis, Elsevier, vol. 199(C).
    • Handle: RePEc:eee:jmvana:v:199:y:2024:i:c:s0047259x23000891
    DOI: 10.1016/j.jmva.2023.105243
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