Rates of Expansions for Functional Estimators

In this paper, we summarize results on convergence rates of various kernel based non- and semiparametric estimators, focusing on the impact of insufficient distributional smoothness, possibly unknown smoothness and even non-existence of density. In the presence of a possible lack of smoothness and the uncertainty about smoothness, methods of safeguarding against this uncertainty are surveyed with emphasis on nonconvex model averaging. This approach can be implemented via a combined estimator that selects weights based on minimizing the asymptotic mean squared error. In order to evaluate the finite sample performance of these and similar estimators we argue that it is important to account for possible lack of smoothness.

A LogTVSCAD Nonconvex Regularization Model for Image Deblurring in the Presence of Impulse Noise

This paper proposes a nonconvex model (called LogTVSCAD) for deblurring images with impulsive noises, using the log-function penalty as the regularizer and adopting the smoothly clipped absolute deviation (SCAD) function as the data-fitting term. The proposed nonconvex model can effectively overcome the poor performance of the classical TVL1 model for high-level impulsive noise. A difference of convex functions algorithm (DCA) is proposed to solve the nonconvex model. For the model subproblem, we consider the alternating direction method of multipliers (ADMM) algorithm to solve it. The global convergence is discussed based on Kurdyka–Lojasiewicz. Experimental results show the advantages of the proposed nonconvex model over existing models.