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Maximum correntropy criterion regression (MCCR) models have been well studiedwithin the frame of statistical learning when the scale parameters take fixedvalues or go to infinity. This paper studies the MCCR models withtending-to-zero scale parameters. It is revealed that the optimal learning rateof MCCR models is ${\mathcal{O}}(n^{-1})$ in the asymptotic sense when thesample size $n$ goes to infinity. In the case of finite samples, theperformances on robustness of MCCR, Huber and the least square regressionmodels are compared. The applications of these three methods on real data arealso displayed.

Maximum Correntropy Criterion Regression models with tending-to-zero scale parameters