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