Synchronizing sample curves nonparametrically

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.