On principal components regression with hilbertian predictors

Jones, Benjamin ORCID: https://orcid.org/0000-0002-6058-9692 and Artemiou, Andreas ORCID: https://orcid.org/0000-0002-7501-4090 2020. On principal components regression with hilbertian predictors. Annals of the Institute of Statistical Mathematics 72 , pp. 627-644. 10.1007/s10463-018-0702-9

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Abstract

We demonstrate that, in a regression setting with a Hilbertian predictor, a response variable is more likely to be more highly correlated with the leading principal components of the predictor than with trailing ones. This is despite the extraction procedure being unsupervised. Our results are established under the conditional independence model, which includes linear regression and single-index models as special cases, with some assumptions on the regression vector. These results are a generalisation of earlier work which showed that this phenomenon holds for predictors which are real random vectors. A simulation study is used to quantify the phenomenon.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Springer Verlag
ISSN:	0020-3157
Date of First Compliant Deposit:	8 November 2018
Date of Acceptance:	6 November 2018
Last Modified:	18 Jan 2025 22:30
URI:	https://orca.cardiff.ac.uk/id/eprint/116541

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