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A note on estimation in Hilbertian linear models. (English) Zbl 1364.62175

Summary: We study estimation and prediction in linear models where the response and the regressor variable both take values in some Hilbert space. Our main objective is to obtain consistency of a principal component-based estimator for the regression operator under minimal assumptions. In particular, we avoid some inconvenient technical restrictions that have been used throughout the literature. We develop our theory in a time-dependent setup that comprises as important special case the autoregressive Hilbertian model.

MSC:

62J05 Linear regression; mixed models
62H25 Factor analysis and principal components; correspondence analysis
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