This paper develops asymptotic normality results for individual coordinates of robust M-estimators with convex penalty in high-dimensions, where the dimension p is at most same order as sample size n, i.e, p∕n≤γ some fixed constant γ>0. The requires a bias correction and holds M-estimator large class loss functions including Huber its smoothed versions regularized strongly penalty. variance tha...

In this paper, we generalize the property of local asymptotic normality (LAN) to an enlarged neighborhood, under name rescaled (RLAN). We obtain sufficient conditions for a regular parametric model satisfy RLAN. show that RLAN supports construction statistically efficient estimator which maximizes cubic approximation log-likelihood on neighborhood. context Monte Carlo inference, find maximum li...