Applied and Computational Mathematics Seminar

Abstract: There are mainly two classes of error variance estimators for nonparametric regression models, the residual-based methods, and the difference-based methods. The latter has gained higher and higher popularity in the past two decades since first introduced by Rice (1984), due to their simplicity in construction and their nice performances. We propose a new residual-based error variance estimator by controlling the amount of cross-validation for the model fit. We demonstrate that the new estimator can achieve better asymptotic rate in the mean squared error(MSE) sense than most existing methods in the literature. We also show that the same bandwidth can be used to estimate both the regression function and the error variance.  Our simulations show that the new estimator provides overall comparable or superior performance in the MSE sense than most existing competitors.