Penalised Euclidean distance regression

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

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.

Citation

Vasiliu, D., Dey, T., & Dryden, I. L. (2018). Penalised Euclidean distance regression. Stat, 7(1), Article e175. https://doi.org/10.1002/sta4.175

• 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