Approximations to the mean integrated squared error with applications to optimal bandwidth selection for nonparametric regression function estimators
type: Item
instance of: scholarly article
title: Approximations to the mean integrated squared error with applications to optimal bandwidth selection for nonparametric regression function estimators
zbMATH Open document ID: 0582.60033
DOI: 10.1016/0047-259X(86)90066-7
published in: Journal of Multivariate Analysis
publication date: 1986-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 62G05
zbMATH DE Number: 3932104
zbMATH Keywords: stochastic measures of accuracy
zbMATH Keywords: Monte Carlo trials
zbMATH Keywords: optimal bandwidth selection
zbMATH Keywords: kernel regression function estimators
author: Wolfgang K. Härdle
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3932104