Uniform Function Estimators in Reproducing Kernel Hilbert Spaces with applications in stochastic optimization
Seminar in Insurance and Economics
SPEAKER: Alois Pichler (TU Chemnitz).
TITLE: Uniform Function Estimators in Reproducing Kernel Hilbert Spaces with applications in stochastic optimization.
ABSTRACT: The talk addresses regression to reconstruct functions, which are observed with superimposed errors at random locations. The problem is considered in reproducing kernel Hilbert spaces (RKHS). It is demonstrated that the estimator, which is often derived by employing Gaussian random fields, converges in the mean norm of the RKHS to the conditional expectation and this implies local and uniform convergence of this function estimator. By preselecting the kernel, the problem does not suffer from the curse of dimensionality. We analyze the statistical properties of the estimator. We derive convergence properties and provide a conservative rate of convergence for increasing sample sizes.