Recent History Functional Linear Models for Sparse Longitudinal Data

• Activity Number: 415
• Type: Contributed
• Date/Time: Tuesday, August 3, 2010 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Kion Kim* and Damla Senturk+
• Companies: Penn State and Penn State
• Keywords: Basis expansion ; functional data analysis ; local least squares ; smoothing ; sparse design

Abstract

We consider the recent history functional linear models, relating a longitudinal response to a longitudinal predictor where the predictor process only in a sliding window into the recent past has an e?ect on the response value at the current time. We propose an estimation procedure for recent history functional linear models that is geared towards sparse longitudinal data, where the observation times across subjects are irregular and total number of measurements per subject is small. The proposed estimation procedure builds upon recent developments for estimation of functional linear models with sparse data and utilizes connections to varying coe?cient models. We establish uniform consistency of the proposed estimators, propose prediction of the response tra jectories and derive their asymptotic distribution leading to asymptotic point-wise con?dence bands.