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

• Activity Number: 92
• Type: Invited
• Date/Time: Sunday, August 9, 2015 : 9:30 PM to 10:15 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Lijie Gu* and Lily Wang and Wolfgang Karl Härdle and Lijian Yang
• Companies: Soochow University and Iowa State University and Humboldt University and Soochow University
• Keywords: B spline ; Confidence corridor ; Karhunen-Loève L2 representation ; Knots ; Functional data ; Varying coefficient

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.