Convergence of generalized cross-validation for an ill-posed integral equation

Abstract

In this article we rigorously show consistency of generalized cross-validation applied to an exemplary ill-posed integral equation, given a finite number of noisy point evaluations. In particular, we present non-asymptotic order-optimal error estimates in probability. Hereby it is remarkable that the unknown true solution is not required to fulfill a self-similarity condition, which is generally needed for other heuristic parameter choice rules.