How Far Are Automatically Chosen Regression Smoothing Parameters from Their Optimum?

· ABSTRACT In the setting of nonparametric curve estimation the problem of smoothing parameter selection is addressed. The deviation between the the squared error optimal smoothing parameter and the smoothing parameters provided by a number of automatic selection methods is studied both theoretically and by simUlation. The theoretical results include a central limit theorem which shows both the rate of convergence and the asymptotic distribution of the deviation. The simulations show that the asymptotic normality describes the distribution quite well for surprisingly small samples.