On linear regression models in infinite dimensional spaces with scalar response
Statistics Theory
2018-01-04 v1 Methodology
Statistics Theory
Abstract
In functional linear regression, the parameters estimation involves solving a non necessarily well-posed problem and it has points of contact with a range of methodologies, including statistical smoothing, deconvolution and projection on finite-dimensional subspaces. We discuss the standard approach based explicitly on functional principal components analysis, nevertheless the choice of the number of basis components remains something subjective and not always properly discussed and justified. In this work we discuss inferential properties of least square estimation in this context with different choices of projection subspaces, as well as we study asymptotic behaviour increasing the dimension of subspaces.
Cite
@article{arxiv.1502.00412,
title = {On linear regression models in infinite dimensional spaces with scalar response},
author = {Andrea Ghiglietti and Francesca Ieva and Anna Maria Paganoni and Giacomo Aletti},
journal= {arXiv preprint arXiv:1502.00412},
year = {2018}
}