Penalised Euclidean distance regressionTools Vasiliu, Daniel and Dey, Tanujit and Dryden, Ian L. (2018) Penalised Euclidean distance regression. Stat, 7 (1). e175/1e175/14. ISSN 20491573
AbstractA 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.
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