L-PASSO: Adaptive Log-penalized Variable Selector, with Sparse Selection and Robustness to the Pilot Estimator

We study L-PASSO, a penalized least-squares regression method based on the logarithmic penalty $λ\sum_j\log(1+|β_j|/τ)$, and its two-stage adaptive form, in which the scales $τ_j$ come from a pilot estimator. Although this concave penalty has been proposed previously, its variable-selection properti