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Penalised Euclidean distance regression

Vasiliu, Daniel; Dey, Tanujit; Dryden, Ian L.

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Authors

Daniel Vasiliu

Tanujit Dey

IAN DRYDEN IAN.DRYDEN@NOTTINGHAM.AC.UK
Professor of Statistics



Abstract

A method is introduced for variable selection and prediction in linear regression problems where the number of predictors can be much larger than the number of observations. The methodology involves minimising a penalised Euclidean distance, where the penalty is the geometric mean of the $\ell_1$ and $\ell_2$ norms of the regression coefficients. This particular formulation exhibits a grouping effect, which is useful for model selection in high dimensional problems. Also, an important result is a model consistency theorem, which does not require an estimate of the noise standard deviation. An algorithm for estimation is described, which involves thresholding to obtain a sparse solution. Practical performances of variable selection and prediction are evaluated through simulation studies and the analysis of real datasets.

Journal Article Type Article
Acceptance Date Dec 3, 2017
Online Publication Date Feb 22, 2018
Publication Date Jan 22, 2018
Deposit Date Dec 13, 2017
Publicly Available Date Jan 22, 2018
Journal Stat
Electronic ISSN 2049-1573
Publisher Wiley
Peer Reviewed Peer Reviewed
Volume 7
Issue 1
Article Number e175
DOI https://doi.org/10.1002/sta4.175
Keywords Euclidean distance; grouping; penalization; prediction; regularization; sparsity; variable screening
Public URL https://nottingham-repository.worktribe.com/output/906522
Publisher URL http://onlinelibrary.wiley.com/doi/10.1002/sta4.175/abstract

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