We introduce a learning algorithm for regression generated by a minimum error entropy (MEE) principle and regularization schemes in reproducing kernel Hilbert spaces. This empirical MEE algorithm is highly related to a scaling parameter arising from Parzen windowing. The purpose of this paper is to carry out consistency analysis when the scaling parameter is large. Explicit learning rates are provided. Novel approaches are proposed to overcome the difficulties in bounding the output function uniformly and in the special MEE feature that the regression function may not be a minimizer of the error entropy.