Asymptotics for statistical functionals of long-memory sequences

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• 作者：Eric Beutnerup>aup>up> ; up>up>e.beutner@maastrichtuniversity.nlup> ; Wei Biao Wuup>bup>up> ; up>up>1up>up> ; up>up>wbwu@galton.uchicago.eduup> ; Henryk Zä ; hleup>cup>up> ; up>up>zaehle@math.uni-sb.deup>
• 关键词：Noncentral limit theorem ; Linear long-memory sequence ; Quasi-Hadamard differentiability ; Modified Functional Delta Method ; Weighted empirical process ; L-statistic ; U- and V-statistics ; Degenerate V-statistic
• 刊名：Stochastic Processes and their Applications
• 出版年：2012
• 期刊代码：57_03044149
• 类别：mt
• 出版时间：March, 2012
• 卷：122
• 期：3
• 页码：910-929
• 文件大小：275 K

摘要

We present two general results that can be used to obtain asymptotic properties for statistical functionals based on linear long-memory sequences. As examples for the first one we consider L- and V-statistics, in particular tail-dependent L-statistics as well as V-statistics with unbounded kernels. As an example for the second result we consider degenerate V-statistics. To prove these results we also establish a weak convergence result for empirical processes of linear long-memory sequences, which improves earlier ones.