Ridge regression revisited: Debiasing, thresholding and bootstrap

The success of the Lasso in era high-dimensional data can be attributed to its conducting an implicit model selection, that is, zeroing out regression coefficients are not significant. By contrast, classical ridge cannot reveal a potential sparsity parameters, and may also introduce large bias under setting. Nevertheless, recent work on involves debiasing thresholding, latter order further enhance selection. As consequence, worth another look since—after thresholding—it offer some advantages over Lasso, for example, it easily computed using closed-form expression. In this paper, we define debiased thresholded method, prove consistency result Gaussian approximation theorem. We wild bootstrap algorithm construct confidence regions perform hypothesis testing linear combination parameters. addition estimation, consider problem prediction, present novel, hybrid tailored prediction intervals. Extensive numerical simulations show has favorable finite sample performance preferable settings.