Inference Methods in Functional Mixed Effects Models

• Activity Number: 338
• Type: Topic Contributed
• Date/Time: Tuesday, August 3, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): David Degras*+
• Companies: The University of Chicago
• Keywords: Functional data ; Mixed-effects model ; Simultaneous confidence bands ; Inference

Abstract

We present a new method for building simultaneous confidence bands (SCB) in functional mixed-effects models. SCB are important graphical and analytic tools used for data exploration, model construction, estimation of fixed and random effects, covariance estimation, prediction, and inference. Our model handles dummy variables and functional predictors. Its nonparametric covariance structure accounts for dependence in the data in a more flexible way than the available models based on smoothing spline or wavelet representations. Our SCB-based method allows to test local and nonparametric alternatives on the model components, as opposed to the usual F-type tests. Some asymptotic theory and a numerical study are presented to support our work and compare it with other approaches currently in practice. Finally we illustrate our methodology with an application to a real data set.