High-Dimensional Variable Selection With Reciprocal L 1 -Regularization

We establish the consistency of the rLasso for variable selection and coefficient estimation under both the low- and high-dimensional settings. Since the rLasso penalty functions induce an objective function with multiple local minima, we also propose an efficient Monte Carlo optimization algorithm to solve the involved minimization problem. Our simulation results show that the rLasso outperforms other popular penalized likelihood methods, such as Lasso, SCAD, minimax concave penalty, sure independence screening, interative sure independence screening, and extended Bayesian information criterion.

It can produce sparser and more accurate coefficient estimates, and catch the true model with a higher probability. Supplementary materials for this article are available online.