Nonlinear system theory: Another look at dependence

Wu WB

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Nonlinear system theory: Another look at dependence

机译：非线性系统理论：另一种依赖关系

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摘要

Based on the nonlinear system theory, we introduce previously undescribed dependence measures for stationary causal processes. Our physical and predictive dependence measures quantify the degree of dependence of outputs on inputs in physical systems. The proposed dependence measures provide a natural framework for a limit theory for stationary processes. In particular, under conditions with quite simple forms, we present limit theorems for partial sums, empirical processes, and kernel density estimates. The conditions are mild and easily verifiable because they are directly related to the data-generating mechanisms.

机译：基于非线性系统理论，我们介绍了平稳因果过程的先前未描述的相关性度量。我们的物理性和预测性依赖度量可量化输出对物理系统中输入的依赖程度。所提出的依赖性度量为平稳过程的极限理论提供了自然的框架。特别是在形式非常简单的条件下，我们给出了部分和，经验过程和核密度估计的极限定理。这些条件是温和的，易于验证，因为它们与数据生成机制直接相关。

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来源
《Proceedings of the National Academy of Sciences of the United States of America》 |2005年第40期|p. 14150-14154|共5页
作者
Wu WB;
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作者单位

Univ Chicago, Dept Stat, Chicago, IL 60637 USA;

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收录信息美国《科学引文索引》(SCI);美国《生物学医学文摘》(MEDLINE);美国《化学文摘》(CA);
原文格式 PDF
正文语种 eng
中图分类自然科学总论;
关键词
nonlinear time series; limit theory; kernel estimation; weak convergence; CENTRAL-LIMIT-THEOREM; STATIONARY-PROCESSES; MOVING AVERAGES; LINEAR-PROCESSES; FUNCTIONALS; STATISTICS; VARIANCE;

机译：非线性时间序列;极限理论;核估计;弱收敛;中心极限定理;平稳过程;移动平均值;线性过程;函数;统计;方差;

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6. Nonlinear system theory: Another look at dependence [O] . Wei Biao Wu 2005

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Nonlinear system theory: Another look at dependence

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