A Note on Estimation in Hilbertian Linear Models. (14th April 2014)

• Record Type: Journal Article
• Authors: Hörmann, Siegfried; Kidziński, Łukasz
• Is Part Of: Scandinavian journal of statistics. Volume 42:Number 1(2015:Mar.)
• Page Start: 43
• Page End: 62
• Publication Date: 2014-04-14
• Subjects: Statistics -- Periodicals; 310
• DOI: 10.1111/sjos.12094
• Languages: English
• ISSNs: 0303-6898

Abstract

<abstract abstract-type="main" id="sjos12094-abs-0001"> <title>Abstract</title> <p>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.</p> </abstract>