## 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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