Approximations to the mean integrated squared error with applications to optimal bandwidth selection for nonparametric regression function estimators
Discrete versions of the mean integrated squared error (MISE) provide stochastic measures of accuracy to compare different estimators of regression functions. These measures of accuracy have been used in Monte Carlo trials and have been employed for the optimal bandwidth selection for kernel regression function estimators, as shown by the author and \textit{J. S. Marron}; [Optimal bandwidth selection in nonparametric regression function estimation. Inst. Stat. Mimeo Ser. No.1530, Univ. North Carolina, Chapel Hill (1983)]. In the present paper it is shown that these stochastic measures of accuracy converge to a weighted version of the MISE of kernel regression function estimators, extending a result of \textit{P. Hall} [Biometrika 69, 383-390 (1982; Zbl 0496.62038)] and \textit{J. S. Marron} [Convergence properties of an empirical error criterion for multivariate density estimation. J. Multivariate Anal. to appear] to regression function estimation.
scientific article; zbMATH DE number 3932104
scientific article