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Incorporating parametric effects into functional principal components analysis. (English) Zbl 0827.62051
Summary: The ideas of functional principal component analysis are extended to deal with data that are hybrids of ‘functional’ and ‘parametric’ effects. The parametric effects may be more general than just the addition of a multiple of a given function. A detailed development is given in the case of shifts of the time axis for functions observed on a periodic interval, and some remarks are made for the extension to a far more general case. Given data, a Procrustes fitting method can be used to estimate the parametric effects. Several possible ways of treating the estimated parameter values are discussed. The methods are illustrated by reference to temperature data at 35 Canadian weather-stations.

MSC:
62H25 Factor analysis and principal components; correspondence analysis
62P99 Applications of statistics
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