Functional Regression and Principal Components Analysis
For Sparse longitudinal Data
Fang Yao
University of California-Davis

Friday, 14 February 2003
3:10 PM
E103 Engineering

We propose a nonparametric method to perform functional regression and principal components analysis for sparse longitudinal data that consist of noisy measurements with underlying smooth random trajectories for each subject in a sample. The number of repeated measurements available per subject is typically small, and their spacing is irregular. Our proposal includes determination of the most appropriate function basis from the data. The proposed conditional method is simple and straightforward to implement and includes estimation of the covariance structure and of the variance of the measurements. It is also suitable for functional regression where both the predictor and response are functions of a covariate such as time. The resulting technique is flexible and allows for different timing of measurements for predictor and response functions.  Asymptotic properties are investigated under mild conditions, using tools from functional analysis.  We illustrate the methods with a simulation study, longitudinal CD4 data in AIDS patients and a functional regression analysis of the dynamic relationship of immunoproteins.
Key Words: Functional Data, Nonparametric Functional Regression,
Refreshments will be served at 2:45 p.m. in Room 008 of the Statistics Building



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