Article ID: | iaor201523761 |
Volume: | 42 |
Issue: | 1 |
Start Page Number: | 43 |
End Page Number: | 62 |
Publication Date: | Mar 2015 |
Journal: | Scandinavian Journal of Statistics |
Authors: | Hrmann Siegfried, Kidzinski Lukasz |
Keywords: | estimation, modelling, Hilbert space |
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.