文章基本信息

标题：Weighted approximations for Studentized $U$-statistics
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作者：Masoud M. Nasari
期刊名称：Brazilian Journal of Probability and Statistics
印刷版ISSN：0103-0752
出版年度：2014
卷号：28
期号：1
页码：24-60
DOI：10.1214/12-BJPS192
语种：English
出版社：Brazilian Statistical Association
摘要：In this article, we employ the jackknife method of estimation and the concept of Studentized $U$-statistics to derive a new weak convergence result for nondegenerate $U$-statistics on the space $D[0,1]$. We drop the classical condition that the second moment of the kernel of the underlying $U$-statistic exists and derive a weighted weak convergence result for these Studentized statistics. This weak convergence is concluded from a weighted approximation in sup-norm $\|/q\|$, in probability, of Studentized $U$-statistics by partial sums of i.i.d. projections, where $q$ is in an appropriate class of positive weight functions.