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June 1997 Alignment of curves by dynamic time warping
Kongming Wang, Theo Gasser
Ann. Statist. 25(3): 1251-1276 (June 1997). DOI: 10.1214/aos/1069362747


When studying some process or development in different subjects or units--be it biological, chemical or physical--we usually see a typical pattern, common to all curves. Yet there is variation both in amplitude and dynamics between curves. Following some ideas of structural analysis introduced by Kneip and Gasser, we study a method--dynamic time warping with a proper cost function--for estimating the shift or warping function from one curve to another to align the two functions. For some models this method can identify the true shift functions if the data are noise free. Noisy data are smoothed by a nonparametric function estimate such as a kernel estimate. It is shown that the proposed estimator is asymptotically normal and converges to the true shift function as the sample size per subject goes to infinity. Some simulation results are presented to illustrate the performance of this method.


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Kongming Wang. Theo Gasser. "Alignment of curves by dynamic time warping." Ann. Statist. 25 (3) 1251 - 1276, June 1997.


Published: June 1997
First available in Project Euclid: 20 November 2003

zbMATH: 0898.62051
MathSciNet: MR1447750
Digital Object Identifier: 10.1214/aos/1069362747

Primary: 62G07
Secondary: 62H05

Keywords: curves , dynamic time warping , Kernel estimation , shift functions , structural analysis

Rights: Copyright © 1997 Institute of Mathematical Statistics


Vol.25 • No. 3 • June 1997
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