A Note on Estimation in Hilbertian Linear Models |
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Authors: | Siegfried Hörmann ?ukasz Kidziński |
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Institution: | Départment de MathématiqueUniversité libre de Bruxelles (ULB) |
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Abstract: | 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. |
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Keywords: | adaptive estimation consistency dependence functional regression Hilbert spaces infinite dimensional data prediction |
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