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

It is known that the classical least square regression models achieve the optimal efficiency when the noises are Gaussian, however, they always underperform if the data is contaminated by non-Gaussian noises or outliers. Some robust regression models have been well developed in the past decades such as the median regression, the modal regression, the Huber regression and the least trimmed squares regression, etc. Moreover, a new robust regression model named the maximum correntropy criterion regression (MCCR) has been theoretically studied within the frame of statistical learning in Feng et al. (2015). Correntropy is constructed based on a kernel function and it is a generalized similarity measure between two random variables (see Santamar ıa et al. (2006); Gunduz and Principe (2009); Liu et al. (2007); He et al. (2011); Chen and Pr ıncipe (2012) 1