On linear regression models in infinite dimensional spaces with scalar response

Andrea Ghiglietti, Francesca Ieva, Anna Maria Paganoni, Giacomo Aletti

Risultato della ricerca: Contributo in rivistaArticolo in rivistapeer review

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.
Lingua originaleEnglish
pagine (da-a)527-548
Numero di pagine22
RivistaStatistical Papers
Volume58
DOI
Stato di pubblicazionePubblicato - 2017

Keywords

  • Asymptotic properties of statistical inference
  • Functional principal component analysis
  • Functional regression

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