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摘要翻译：
引入局部统计过程的概念，得到了局部统计过程在各种范数下的中心极限定理。这涉及到为$u$-过程开发几个不等式，这些不等式在其他上下文中可能很有用。这个局部的$u$-统计过程是基于Frees[J.Amer.Statist.Assoc.89(1994)517-525]提出的若干样本变量函数密度的估计量，因此，对于这些估计量，在sup和$l_p$范数中得到了一致的带宽中心极限定理。
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英文标题：
《On local $U$-statistic processes and the estimation of densities of
functions of several sample variables》
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作者：
Evarist Gin\'e, David M. Mason
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
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.
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PDF链接：
https://arxiv.org/pdf/708.2227
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