M-based simultaneous inference for the mean function of functional data

  • Italo R. Lima
  • Guanqun CaoEmail author
  • Nedret Billor


Estimating and constructing a simultaneous confidence band for the mean function in the presence of outliers is an important problem in the framework of functional data analysis. In this paper, we propose a robust estimator and a robust simultaneous confidence band for the mean function of functional data using M-estimation and B-splines. The robust simultaneous confidence band is also extended to the difference of mean functions of two populations. Further, the asymptotic properties of the M-based mean function estimator, such as the asymptotic consistency and asymptotic normality, are studied. The performance of the proposed robust methods and their robustness are demonstrated with an extensive simulation study and two real data examples.


Confidence band Functional data analysis Robust statistics Spline smoothing M-estimator Pseudo-data 

Supplementary material

10463_2018_656_MOESM1_ESM.pdf (250 kb)
Supplementary material 1 (pdf 249 KB)


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Copyright information

© The Institute of Statistical Mathematics, Tokyo 2018

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsAuburn UniversityAuburnUSA

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