On local $U$-statistic processes and the estimation of densities of functions of several sample variables

Evarist Giné; David M. Mason

doi:10.1214/009053607000000154

On local $U$-statistic processes and the estimation of densities of functions of several sample variables

Statistics Theory 2009-09-29 v1 Statistics Theory

Authors: Evarist Giné , David M. Mason

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Abstract

A notion of local $U$ -statistic process is introduced and central limit theorems in various norms are obtained for it. This involves the development of several inequalities for $U$ -processes that may be useful in other contexts. This local $U$ -statistic process is based on an estimator of the density of a function of several sample variables proposed by Frees [J. Amer. Statist. Assoc. 89 (1994) 517--525] and, as a consequence, uniform in bandwidth central limit theorems in the sup and in the $L_p$ norms are obtained for these estimators.

Keywords

local $U$-statistic process central limit theorems density estimation functions of several sample variables uniform in bandwidth $L_p$ norms sup norms

Cite

@article{arxiv.0708.2227,
  title  = {On local $U$-statistic processes and the estimation of densities of functions of several sample variables},
  author = {Evarist Giné and David M. Mason},
  journal= {arXiv preprint arXiv:0708.2227},
  year   = {2009}
}

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Published at http://dx.doi.org/10.1214/009053607000000154 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

On local $U$-statistic processes and the estimation of densities of functions of several sample variables

Abstract

Keywords

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