On Local U-Statistic Processes and the Estimation of Densities of Functions of Several Sample Variables

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...

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Veröffentlicht in:The Annals of statistics 2007-07, Vol.35 (3), p.1105-1145
Hauptverfasser: Giné, Evarist, Mason, David M.
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:0090-5364
2168-8966
DOI:10.1214/009053607000000154