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Curve registration. (English) Zbl 0909.62033
Summary: 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.

MSC:
62G07 Density estimation
62M99 Inference from stochastic processes
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