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