Nonparametric estimation of quadratic regression functionals

Quadratic regression functionals are important for bandwidth selection of n onparametric regression techniques and for nonparametric goodness-of-fit te sts. Based on local polynomial regression, we propose estimators for weight ed integrals of squared derivatives of regression functions. The rates of c onvergence in mean square error are calculated under various degrees of smo othness and appropriate values of the smoothing parameter. Asymptotic distr ibutions of the proposed quadratic estimators are considered with the Gauss ian noise assumption. It is shown that when the estimators are pseudo-quadr atic (linear components dominate quadratic components), asymptotic normalit y with rate n(-1/2) can be achieved.