Uniform Function Estimators in Reproducing Kernel Hilbert Spaces

This paper addresses the problem of regression and approximation, nowadays occasionally often associated with the term statistical learning. The specific estimator we consider is based on kernel functions. We investigate the estimator's convergence properties in the the genuine and most natural norm, the norm induced by the kernel function itself. The estimator is often derived by involving Gaussian random fields and is central in support vector machines as well, an additional motivational point to investigate its specific properties. Here, the estimator is often inferred with least squares errors and by involving a regularization term based on a reproducing kernel Hilbert space.