A Note on Estimation in Hilbertian Linear Models

Siegfried Hörmann and Łukasz Kidziński

Scandinavian Journal of Statistics, 2015, vol. 42, issue 1, 43-62

Abstract: type="main" xml:id="sjos12094-abs-0001">

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.

Date: 2015
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