Maximum correntropy criterion regression models with tending-to-zero scale parameters

Maximum correntropy criterion regression (MCCR) models have been well studied within the theoretical framework of statistical learning when the scale parameters take fixed values or go to infinity. This paper studies MCCR models with tending-to-zero scale parameters. It is revealed that the optimal learning rate of MCCR models is $O\left(n^{-1}\right)$ in the asymptotic sense when the sample size $n$ goes to infinity. In the case of finite samples, the performance and robustness of MCCR, Huber and the least square regression models are compared. The applications of these three methods to real data are also demonstrated.