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Simultaneous confidence band for stationary covariance function of dense functional data

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  • Wang, Jiangyan
  • Cao, Guanqun
  • Wang, Li
  • Yang, Lijian

Abstract

The inference via simultaneous confidence band is studied for stationary covariance function of dense functional data. A two-stage estimation procedure is proposed based on spline approximation, the first stage involving estimation of all the individual trajectories and the second stage involving estimation of the covariance function through smoothing the empirical covariance function. The proposed covariance estimator is smooth and as efficient as the oracle estimator when all individual trajectories are known. An asymptotic simultaneous confidence band (SCB) is developed for the true covariance function, and the coverage probabilities are shown to be asymptotically correct. Intensive simulation experiments are conducted to demonstrate the performance of the proposed estimator and SCB. The proposed method is also illustrated with a real data example.

Suggested Citation

  • Wang, Jiangyan & Cao, Guanqun & Wang, Li & Yang, Lijian, 2020. "Simultaneous confidence band for stationary covariance function of dense functional data," Journal of Multivariate Analysis, Elsevier, vol. 176(C).
    • Handle: RePEc:eee:jmvana:v:176:y:2020:i:c:s0047259x19301423
    DOI: 10.1016/j.jmva.2019.104584
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    References listed on IDEAS

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    Cited by:

    1. Kun Huang & Sijie Zheng & Lijian Yang, 2022. "Inference for dependent error functional data with application to event-related potentials," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(4), pages 1100-1120, December.
    2. Li, Yehua & Qiu, Yumou & Xu, Yuhang, 2022. "From multivariate to functional data analysis: Fundamentals, recent developments, and emerging areas," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    3. Cai, Leheng & Hu, Qirui, 2024. "Simultaneous inference and uniform test for eigensystems of functional data," Computational Statistics & Data Analysis, Elsevier, vol. 192(C).
    4. Telschow, Fabian J.E. & Davenport, Samuel & Schwartzman, Armin, 2022. "Functional delta residuals and applications to simultaneous confidence bands of moment based statistics," Journal of Multivariate Analysis, Elsevier, vol. 192(C).

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