THE FUNCTIONAL LIMIT THEOREM FOR THE CANONICAL U-PROCESSES DEFINED ON DEPENDENT TRIALS

I. S. Borisov; V. A. Zhechev

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THE FUNCTIONAL LIMIT THEOREM FOR THE CANONICAL U-PROCESSES DEFINED ON DEPENDENT TRIALS

机译：在相关试验中定义的规范U过程的函数极限定理

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摘要

The functional limit theorem is proven for a sequence of normalized U-statistics (the socalled U-processes) of arbitrary order with canonical (degenerate) kernels defined on samples of -mixing observations of growing size. The corresponding limit distribution is described as that of a polynomial of a sequence of dependent Wiener processes with some known covariance function.

机译：证明了函数极限定理适用于任意阶数的正规化U统计量（所谓的U过程），具有在增长的混合观测样本上定义的规范（简并）核。相应的极限分布被描述为具有某些已知协方差函数的一系列相关维纳过程的多项式的分布。

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《Siberian Mathematical Journal》 |2011年第4期|共9页
作者
I. S. Borisov; V. A. Zhechev;
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原文格式 PDF
正文语种 eng
中图分类数学;
关键词
canonical U-statistics; invariance principle; stationary sequence of observations; mixing;

机译：规范的U统计量;不变性原理;平稳观测序列;混合;

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1. THE FUNCTIONAL LIMIT THEOREM FOR THE CANONICAL U-PROCESSES DEFINED ON DEPENDENT TRIALS [J] . I. S. Borisov, V. A. Zhechev Siberian Mathematical Journal . 2011,第4期

机译：在相关试验中定义的规范U过程的函数极限定理
2. Limit theorems for the canonical von Mises statistics with dependent data [J] . I. S. Borisov, A. A. Bystrov Siberian Mathematical Journal . 2006,第6期

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8. Central Limit Theorems for Empirical and U-Processes of Stationary MixingSequences [R] . Arcones, M. A., Yu, B. 1994

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THE FUNCTIONAL LIMIT THEOREM FOR THE CANONICAL U-PROCESSES DEFINED ON DEPENDENT TRIALS

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