, Volume 23, Issue 4, pp 806–843 | Cite as

A simultaneous confidence corridor for varying coefficient regression with sparse functional data

  • Lijie Gu
  • Li Wang
  • Wolfgang K. Härdle
  • Lijian YangEmail author
Original Paper


We consider a varying coefficient regression model for sparse functional data, with time varying response variable depending linearly on some time-independent covariates with coefficients as functions of time-dependent covariates. Based on spline smoothing, we propose data-driven simultaneous confidence corridors for the coefficient functions with asymptotically correct confidence level. Such confidence corridors are useful benchmarks for statistical inference on the global shapes of coefficient functions under any hypotheses. Simulation experiments corroborate with the theoretical results. An example in CD4/HIV study is used to illustrate how inference is made with computable p values on the effects of smoking, pre-infection CD4 cell percentage and age on the CD4 cell percentage of HIV infected patients under treatment.


B spline Confidence corridor Karhunen–Loève \(L^{2}\) representation Knots Functional data Varying coefficient 

Mathematics Subject Classification (2000)

62G08 62G15 62G32 



This work is part of Lijie Gu’s dissertation and has been supported in part by the Deutsche Forschungsgemeinschaft through the CRC 649 “Economic Risk”, the US National Science Foundation awards DMS 0905730, 1007594, 1106816, 1309800, Jiangsu Specially Appointed Professor Program SR10700111, Jiangsu Province Key-Discipline Program (Statistics) ZY107002, National Natural Science Foundation of China award 11371272, and Research Fund for the Doctoral Program of Higher Education of China award 20133201110002.


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Copyright information

© Sociedad de Estadística e Investigación Operativa 2014

Authors and Affiliations

  • Lijie Gu
    • 1
  • Li Wang
    • 2
  • Wolfgang K. Härdle
    • 3
    • 4
  • Lijian Yang
    • 1
    Email author
  1. 1.Center for Advanced Statistics and Econometrics ResearchSoochow UniversitySuzhouChina
  2. 2.Department of StatisticsIowa State UniversityAmesUSA
  3. 3.Center for Applied Statistics and Economics (C.A.S.E.)Humboldt-Universität zu BerlinBerlinGermany
  4. 4.Lee Kong Chian School of BusinessSingapore Management UniversitySingaporeSingapore

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