Regularization for Regression Models Based on the K-Functional with Besov Norm

摘要

This paper presents a new method of regularization in regression problems using a Besov norm (or semi-norm) acting as a regularization operator. This norm is more general smoothness measure to approximation spaces compared to other norms such as Sobolev and RKHS norms which are usually used in the conventional regularization methods. In our work, we also suggest a new candidate of the regularization parameter, that is, the trade-off between the data fit and the smoothness of the estimation function. Through the simulation for function approximation, we have shown that the suggested regularization method is effective and the estimated values of regularization parameters are close to the optimal values associated with the minimum expected risks.