TEST

, Volume 23, Issue 4, pp 806–843

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

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

DOI: 10.1007/s11749-014-0392-4

Cite this article as:
Gu, L., Wang, L., Härdle, W.K. et al. TEST (2014) 23: 806. doi:10.1007/s11749-014-0392-4

Abstract

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.

Keywords

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

Mathematics Subject Classification (2000)

62G08 62G15 62G32 

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
  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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