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.

Ghiglietti, A., Ieva, F., Paganoni, A. M., Aletti, G., On linear regression models in infinite dimensional spaces with scalar response, <<STATISTICAL PAPERS>>, 2017; 58 (2): 527-548. [doi:10.1007/s00362-015-0710-2] [http://hdl.handle.net/10807/109394]

On linear regression models in infinite dimensional spaces with scalar response

Ghiglietti, Andrea
Primo
;
2017

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.
Inglese
Ghiglietti, A., Ieva, F., Paganoni, A. M., Aletti, G., On linear regression models in infinite dimensional spaces with scalar response, <<STATISTICAL PAPERS>>, 2017; 58 (2): 527-548. [doi:10.1007/s00362-015-0710-2] [http://hdl.handle.net/10807/109394]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10807/109394
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