Asymptotic Properties of Generalized Cross Validation Estimators for Regularized System Identification ?

摘要

In this paper, we study the asymptotic properties of the generalized cross validation (GCV) hyperparameter estimator and establish its connection with the Stein’s unbiased risk estimators (SURE) as well as the mean squared error (MSE). It is shown that as the number of data goes to infinity, the GCV has the same asymptotic property as the SURE does and both of them converge to the best hyperparameter in the MSE sense. We illustrate the efficacy of the result by Monte Carlo simulations.