A note on estimation in Hilbertian linear models

Siegfried Hörmann, Lukasz Kidziski

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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.
Original languageUndefined/Unknown
Pages (from-to)43-62
Number of pages20
JournalScandinavian Journal of Statistics
Issue number1
Publication statusPublished - 2015

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