Nonpenalized variable selection in high-dimensional linear model settings via generalized fiducial inference (Q2414104)

This article develops a new perspective on variable selection to deal with linear dependences among subsets of covariates in a high-dimensional setting. A generalized fiducial inference framework is adopted. A procedure to assign small probabilities to subsets of covariates which include redundancies by way of explicit Lo minimization using a Dantzig selector approach is presented. A concept of $\varepsilon$-admissible subsets is proposed to give rise to the determination of a posterior-like distribution which assigns negligible probabilities to all subsets with redundancies in the true data generating model. It is shown that, under a typical sparsity condition, the probability of the true data generating model converges to 1. Comparisons with Bayesian and frequentist methods are performed in two simulation setups.