This is the program for the 2010 Joint Statistical Meetings in Vancouver, British Columbia.

Abstract Details

Activity Number: 661
Type: Topic Contributed
Date/Time: Thursday, August 5, 2010 : 10:30 AM to 12:20 PM
Sponsor: Section on Nonparametric Statistics
Abstract - #307595
Title: Thresholded Projection Estimator for the Mean Function in Functional Data
Author(s): Florentina Bunea and Marten Wegkamp and Andrada Ivanescu*+
Companies: Florida State University and Florida State University and East Carolina University
Address: , , ,
Keywords: nonparametric mean estimation ; thresholded estimator ; uniform confidence bands ; functional data ; stochastic processes
Abstract:

We propose and analyze a data driven method for estimating the mean function of a stochastic process from a sample of trajectories of the process, observed at random time points and corrupted by additive random error. The proposed method uses thresholded least squares estimators relative to an approximating function basis. The variable threshold levels are estimated from the data and the resulting estimate adapts to the unknown sparsity of the mean function relative to the selected approximating basis. In addition, we construct confidence bands that adapt to the unknown regularity of the mean function. The simulation study that complements the theoretical results shows that the new method performs very well in practice, and is robust against large variations introduced by the random error terms.


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