On linear regression models in infinite dimensional spaces with scalar response

Andrea Ghiglietti (), Francesca Ieva (), Anna Maria Paganoni () and Giacomo Aletti ()
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Andrea Ghiglietti: Università degli Studi di Milano
Francesca Ieva: Università degli Studi di Milano
Anna Maria Paganoni: Politecnico di Milano
Giacomo Aletti: Università degli Studi di Milano

Statistical Papers, 2017, vol. 58, issue 2, No 12, 527-548

Abstract: Abstract In functional linear regression, the parameters estimation involves solving a non necessarily well-posed problem, which 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.

Keywords: Functional regression; Functional principal component analysis; Asymptotic properties of statistical inference; 62J05; 62M10 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s00362-015-0710-2

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