Open Access
December, 1988 Strong Uniform Consistency Rates for Estimators of Conditional Functionals
W. Hardle, P. Janssen, R. Serfling
Ann. Statist. 16(4): 1428-1449 (December, 1988). DOI: 10.1214/aos/1176351047


Strong uniform consistency rates are established for kernel type estimators of functionals of the conditional distribution function, under general conditions. The present treatment unifies a number of specific problems previously studied separately in the literature. Some of these applications we treat in detail, including regression curve estimation, density estimation, estimation of conditional df's, $L$-smoothing and $M$-smoothing. Various previous results in the literature are extended and/or sharpened.


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W. Hardle. P. Janssen. R. Serfling. "Strong Uniform Consistency Rates for Estimators of Conditional Functionals." Ann. Statist. 16 (4) 1428 - 1449, December, 1988.


Published: December, 1988
First available in Project Euclid: 12 April 2007

zbMATH: 0672.62050
MathSciNet: MR964932
Digital Object Identifier: 10.1214/aos/1176351047

Primary: 62G05
Secondary: 60F15

Keywords: $L$-smoother , $M$-smoother , Density estimation , nonparametric kernel estimators , regression function estimation , Strong uniform consistency rates

Rights: Copyright © 1988 Institute of Mathematical Statistics

Vol.16 • No. 4 • December, 1988
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