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The success of the Lasso in the era of high-dimensional data can beattributed to its conducting an implicit model selection, i.e., zeroing outregression coefficients that are not significant. By contrast, classical ridgeregression can not reveal a potential sparsity of parameters, and may alsointroduce a large bias under the high-dimensional setting. Nevertheless, recentwork on the Lasso involves debiasing and thresholding, the latter in order tofurther enhance the model selection. As a consequence, ridge regression may beworth another look since -- after debiasing and thresholding -- it may offersome advantages over the Lasso, e.g., it can be easily computed using aclosed-form expression. % and it has similar performance to threshold Lasso. Inthis paper, we define a debiased and thresholded ridge regression method, andprove a consistency result and a Gaussian approximation theorem. We furtherintroduce a wild bootstrap algorithm to construct confidence regions andperform hypothesis testing for a linear combination of parameters. In additionto estimation, we consider the problem of prediction, and present a novel,hybrid bootstrap algorithm tailored for prediction intervals. Extensivenumerical simulations further show that the debiased and thresholded ridgeregression has favorable finite sample performance and may be preferable insome settings.

Ridge Regression Revisited: Debiasing, Thresholding and Bootstrap