A note on estimation in Hilbertian linear models

Siegfried Hörmann, Lukasz Kidziski

Research output: Contribution to journalArticle

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.
Original languageUndefined/Unknown
Pages (from-to)43-62
Number of pages20
JournalScandinavian journal of statistics
Volume42
Issue number1
Publication statusPublished - 2015

Cite this