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This paper discusses the selection of the smoothing parameter necessary to implement a penalized regression using a nonconcave penalty function. The proposed method can be derived from a Bayesian viewpoint, and the resultant smoothing parameter is guaranteed to satisfy the sucient conditions for the oracle properties of a one-step estimator. The results of simulation and application to some real data sets reveal that our proposal works eciently, especially for discrete outputs.

Selection of Smoothing Parameter for One-Step Sparse Estimates with Lq Penalty