Kozek, AYin, Jiying2015-12-130167-9473http://hdl.handle.net/1885/81621New estimators of expected values Ew(X) of functions of a random variable X are introduced. The new estimators are based on Gauss quadrature, a numerical method frequently used to approximate integrals over finite intervals. The estimators need a small number of numerical evaluations and hence are useful in partial cross validation (PCV) a numerical method for finding optimal smoothing parameters in nonparametric curve estimation. The PCV can considerably reduce the computational cost of the generalized cross validation method typically used to determine the optimal smoothing parameter.Keywords: Approximation theory; Data reduction; Estimation; Numerical methods; Optimization; Computational costs; Finite intervals; Computational methods; regression analysis; statistical analysis Asymptotic distributions; Cross-validation; Fast statistical methods; Gauss quadrature; Nonparametric regression; Smoothing200410.1016/S0167-9473(03)00040-92015-12-11