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Biometrika Advance Access published online on November 5, 2008
Biometrika, doi:10.1093/biomet/asn047
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© 2008 Biometrika Trust

Article

Pairwise curve synchronization for functional data

Rong Tang

Division of Biostatistics, Center for Devices and Radiological Health, Food and Drug Administration, Rockville, Maryland 20850, U.S.A. rong.tang{at}fda.hhs.gov

Hans-Georg Müller

Department of Statistics, University of California, Davis, California 95616, U.S.A. mueller{at}wald.ucdavis.edu

Received for publication 1 May 2007. Revision received 1 April 2008.
  Abstract

Data collected by scientists are increasingly in the form of trajectories or curves. Often these can be viewed as realizations of a composite process driven by both amplitude and time variation. We consider the situation in which functional variation is dominated by time variation, and develop a curve-synchronization method that uses every trajectory in the sample as a reference to obtain pairwise warping functions in the first step. These initial pairwise warping functions are then used to create improved estimators of the underlying individual warping functions in the second step. A truncated averaging process is used to obtain robust estimation of individual warping functions. The method compares well with other available time-synchronization approaches and is illustrated with Berkeley growth data and gene expression data for multiple sclerosis.

Key Words: Alignment • Curve registration • Functional data analysis • Gene expression profile • Multiple sclerosis • Synchronization • Time warping


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