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A Simultaneous Confidence Corridor for Varying Coefficient Regression with Sparse Functional Data

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  • Lijie Gu
  • Li Wang
  • Wolfgang Karl Härdle
  • Lijian Yang

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, preinfection CD4 cell percentage and age on the CD4 cell percentage of HIV infected patients under treatment.

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Bibliographic Info

Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2014-002.

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Length: 48 pages
Date of creation: Jan 2014
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Handle: RePEc:hum:wpaper:sfb649dp2014-002

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Keywords: B spline; confidence corridor; Karhunen-Loève L^2 representation; knots; functional data; varying coefficient;

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  1. Lan Zhou & Jianhua Z. Huang & Raymond J. Carroll, 2008. "Joint modelling of paired sparse functional data using principal components," Biometrika, Biometrika Trust, Biometrika Trust, vol. 95(3), pages 601-619.
  2. Yao, Fang & Muller, Hans-Georg & Wang, Jane-Ling, 2005. "Functional Data Analysis for Sparse Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 100, pages 577-590, June.
  3. Weixin Yao & Runze Li, 2013. "New local estimation procedure for a non-parametric regression function for longitudinal data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, Royal Statistical Society, vol. 75(1), pages 123-138, 01.
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