The Annals of Statistics

Strong Uniform Consistency Rates for Estimators of Conditional Functionals

W. Hardle, P. Janssen, and R. Serfling

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Abstract

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.

Article information

Source
Ann. Statist., Volume 16, Number 4 (1988), 1428-1449.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176351047

Digital Object Identifier
doi:10.1214/aos/1176351047

Mathematical Reviews number (MathSciNet)
MR964932

Zentralblatt MATH identifier
0672.62050

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation
Secondary: 60F15: Strong theorems

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

Citation

Hardle, W.; Janssen, P.; Serfling, R. Strong Uniform Consistency Rates for Estimators of Conditional Functionals. Ann. Statist. 16 (1988), no. 4, 1428--1449. doi:10.1214/aos/1176351047. https://projecteuclid.org/euclid.aos/1176351047


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