A Note on Estimation in Hilbertian Linear Models

• Autores: Siegfried Hörmann, Łukasz Kidziński
• Localización: Scandinavian journal of statistics: Theory and applications, ISSN 0303-6898, Vol. 42, Nº. 1, 2015, págs. 43-62
• Idioma: inglés
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• Resumen

  • 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.