A Note on Estimation in Hilbertian Linear Models

A Note on Estimation in Hilbertian Linear Models

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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: ,
Keywords: estimation, modelling, Hilbert space
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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