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A Simultaneous Confidence Band for Dense Longitudinal Regression

Author

Listed:
  • Q. Song
  • R. Liu
  • Q. Shao
  • L. Yang

Abstract

We present a method of using local linear smoothing to construct simultaneous confidence bands for the mean function of densely spaced functional data. Our approach works well under mild conditions. In addition, the local linear estimator and its accompanying confidence band enjoy semiparametric efficiency in the sense that they are asymptotically equivalent to the counterparts obtained from the random trajectories entirely observed without errors. We illustrate the performance of the proposed confidence band through a simulation study. Furthermore, an application in food science is presented.

Suggested Citation

  • Q. Song & R. Liu & Q. Shao & L. Yang, 2014. "A Simultaneous Confidence Band for Dense Longitudinal Regression," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(24), pages 5195-5210, December.
    • Handle: RePEc:taf:lstaxx:v:43:y:2014:i:24:p:5195-5210
    DOI: 10.1080/03610926.2012.729643
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    Cited by:

    1. Cao, Guanqun & Wang, Li, 2018. "Simultaneous inference for the mean of repeated functional data," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 279-295.
    2. Jie Li & Jiangyan Wang & Lijian Yang, 2022. "Kolmogorov–Smirnov simultaneous confidence bands for time series distribution function," Computational Statistics, Springer, vol. 37(3), pages 1015-1039, July.
    3. Wang, Jiangyan & Gu, Lijie & Yang, Lijian, 2022. "Oracle-efficient estimation for functional data error distribution with simultaneous confidence band," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    4. Jiangyan Wang & Suojin Wang & Lijian Yang, 2016. "Simultaneous confidence bands for the distribution function of a finite population and of its superpopulation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(4), pages 692-709, December.
    5. Yuanyuan Zhang & Lijian Yang, 2018. "A smooth simultaneous confidence band for correlation curve," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(2), pages 247-269, June.
    6. Chen Zhong & Lijian Yang, 2021. "Simultaneous confidence bands for comparing variance functions of two samples based on deterministic designs," Computational Statistics, Springer, vol. 36(2), pages 1197-1218, June.
    7. Lijie Gu & Suojin Wang & Lijian Yang, 2019. "Simultaneous confidence bands for the distribution function of a finite population in stratified sampling," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(4), pages 983-1005, August.

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