Simultaneous Confidence Bands for Derivative Functions in Repeated Functional Data

• Activity Number: 463
• Type: Contributed
• Date/Time: Wednesday, August 6, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Guanqun Cao*+
• Companies: Auburn University
• Keywords: Functional Data ; Spline smoothing ; semiparametric efficiency

Abstract

This work considers the problem of developing confidence bands for derivatives of the mean curves in repeated functional data analysis. In this situation, curves are recorded repeatedly for each subject in a sample and thus they are dependent functional data. To construct the band, polynomial splines are employed to approximate the derivatives of the mean functions. The semiparametric efficiency is achieved for the derivative estimators of mean curves. The proposed spline simultaneous confidence bands are shown to be asymptotically correct by taking into account the correlation of trajectories within subjects. We illustrate the finite sample properties of the proposed confidence bands by simulation studies and the real data analysis.