Strong Uniform Consistency Rates for Estimators of Conditional Functionals
W. Hardle, P. Janssen, R. Serfling
The Annals of Statistics · 1988 · Volume 16 · Issue 4
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.
Keywords
$L$-smoother, $M$-smoother, 60F15, 62G05, Density estimation, nonparametric kernel estimators, regression function estimation, Strong uniform consistency rates
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