On Gauss quadrature and partial cross validation

In the paper we consider new estimators of expected values E w(X) of functions of a random variable X. The new estimators are based on Gauss quadrature, a numerical method frequently used to approximate integrals over finite intervals. We apply the new estimators in Partial Cross Validation, a numerical method for finding optimal smoothing parameters in nonparametric curve estimation. We show that Partial Cross Validation can considerably reduce the computational cost of the Generalized Cross Validation method typically used to determine the optimal smoothing parameter.