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Activity Number: 128
Type: Contributed
Date/Time: Monday, August 10, 2015 : 8:30 AM to 10:20 AM
Sponsor: International Indian Statistical Association
Abstract #316101 View Presentation
Title: Tolerance Bands for Functional Data
Author(s): Lasitha Rathnayake* and Pankaj Choudhary
Companies: and The University of Texas at Dallas
Keywords: Bootstrap ; functional data analysis ; functional principal component analysis ; mixed model ; tolerance interval
Abstract:

Often the object of inference in biomedical and engineering applications is a population interval that brackets a given large fraction of individual observations. A classical estimate of this interval for univariate observations is a `tolerance interval.' Its natural extension for functional observations is a `tolerance band.' We propose a methodology for constructing pointwise and simultaneous tolerance bands. The methodology uses functional principal component analysis in a mixed model framework to decompose and represent the functional observations, and employs bootstrap to approximate the critical points needed for the tolerance bands. It also applies a correction to the bands to account for uncertainty in the principal components decomposition. Simulations show that the methodology works reasonably well with moderately large number of subjects for both dense and sparse data. Its application is illustrated using a real dataset involving CD4 cell counts.


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