A Quadratic Approximation Approach on Penalized Estimations

Abstract

Non-convex penalized estimations have many desirable properties including the oracle property: asymptotic equivalence between the penalized estimator and the true unknown non-penalized estimator. In this paper, we study a quadratic approximation framework studied by (Kwon et al., 2010) for a class of penalties that includes the smoothly clipped absolute deviation (SCAD) and minimax concave penalty (MCP) as special cases. Theoretically, the driven estimator is asymptotically equivalent to the original one so that the oracle property can be preserved up to a diverging number of parameters. Two numerical studies confirm the efficiency of the orcle, ordinary, SCAD, Q-SCAD, MCP, Q-MCP and LSA estimators.