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doi:10.1111/1467-9868.00129

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2002-01-06

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DOI：10.1111/1467-9868.00129

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Functional data analysis involves the extension of familiar statistical procedures such as principal components analysis, linear modelling and canonical correlation analysis to data where the raw observation x(i) is a function. An essential preliminary to a functional data analysis is often the registration or alignment of salient curve features by suitable monotone transformations h(i) of the argument t, so that the actual analyses are carried out on the values x(i){h(i)( t)}. This is referred to as dynamic time warping in the engineering literature. In effect, this conceptualizes variation among functions as being composed of two aspects: horizontal and vertical, or domain and range. A nonparametric function estimation technique is described for identifying the smooth monotone transformations h(i) and is illustrated by data analyses. A second-order linear stochastic differential equation is proposed to model these components of variation.

Keyword:

dynamic time warping

geometric Brownian motion

monotone functions

spline

stochastic time

time warping

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