JSM 2011 Online Program

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Abstract Details

Activity Number: 386
Type: Invited
Date/Time: Tuesday, August 2, 2011 : 2:00 PM to 3:50 PM
Sponsor: General Methodology
Abstract - #300206
Title: Spline Confidence Envelopes for Covariance Function in Dense Functional/Longitudinal Data
Author(s): Guanqun Cao*+ and Li Wang and Yehua Li and Lijian Yang
Companies: Michigan State University and University of Georgia and University of Georgia and Michigan State University
Address: , East Lansing, MI, 48824,
Keywords: B spline ; confidence envelope ; covariance function ; functional data ; Karhunen-Loeve L2 representation ; longitudinal data
Abstract:

We consider nonparametric estimation of the covariance function for dense functional data using tensor product B-splines. The proposed estimator is computationally more efficient than the kernel-based methods. We develop both local and global asymptotic distributions for the proposed estimator, and show that our estimator is as efficient as an oracle estimator where the true mean function is known. Simultaneous confidence envelopes are developed based on asymptotic theory to quantify the variability in the covariance estimator and to make global inferences on the true covariance. Monte Carlo simulation experiments provide strong evidence that corroborates the asymptotic theory. A real data example on Tecator infrared spectroscopy data is also provided to illustrate the proposed method.


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