Empirical processes of long-memory sequences
Empirical processes of long-memory sequences
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DOI：
10.3150/bj/1066418879
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发表时间：
2003-10
期刊：
影响因子：
1.5
通讯作者：
W. Wu
中科院分区：
文献类型：
--
作者：
W. Wu
研究了以分段可微泛函为指标的长记忆序列的渐近展开式，给出了这些泛函的外期望的上界。这些结果与独立随机变量经验过程的经典理论有着显著的不同。我们的结果超越了早期的允许更广泛的功能类，以及提出更清晰的界限，从而提供了一个更通用的方法相关的统计推断。给出了指示函数类经验过程的完整刻画。讨论了M -估计的应用.
Asymptotic expansions of long-memory sequences indexed by piecewise differentiable functionals are investigated and upper bounds of outer expectations of those functionals are given. These results differ strikingly from the classical theories of empirical processes of independent random variables. Our results go beyond earlier ones by allowing wider function classes as well as by presenting sharper bounds, and thus provide a more versatile approach for related statistical inferences. A complete characterization of empirical processes for indicator function class is presented. Application to M -estimation is discussed.