The Annals of Statistics

Synchronizing sample curves nonparametrically

Theo Gasser and Kongming Wang

Full-text: Open access

Abstract

More and more often, the outcome of a study is not a random variable but a noisy function for each experimental unit, resulting in a sample of curves. Typically, the individual curves vary not only in amplitude or intensity, but also with respect to the time axis: different subjects experience certain events sooner or later. Analyzing such data involves finding out the time changes (or curve registration) among curves. Following our previous work where modified dynamic time warping is applied to align two curves, we formulate a global minimization problem to align all curves in a sample and to compute the aligned average curve. Algorithms for solving the minimization problem are presented and tested with simulated and real data. The test results are promising. The method, which involves kernel smoothing of regression functions, estimates the time changes and the average of the aligned curves from noisy data. Large sample asymptotics is derived.

Article information

Source
Ann. Statist., Volume 27, Number 2 (1999), 439-460.

Dates
First available in Project Euclid: 5 April 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1018031202

Digital Object Identifier
doi:10.1214/aos/1018031202

Mathematical Reviews number (MathSciNet)
MR1714722

Zentralblatt MATH identifier
0942.62043

Subjects
Primary: 62G07: Density estimation
Secondary: 62H05: Characterization and structure theory

Keywords
Curves dynamic time warping kernel estimation structural analysis warping functions.

Citation

Wang, Kongming; Gasser, Theo. Synchronizing sample curves nonparametrically. Ann. Statist. 27 (1999), no. 2, 439--460. doi:10.1214/aos/1018031202. https://projecteuclid.org/euclid.aos/1018031202


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