Nonlinear System Theory: Another Look at Dependence

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 natura...

Ausführliche Beschreibung

Bibliographische Detailangaben
Veröffentlicht in:	Proceedings of the National Academy of Sciences of the United States of America. - National Academy of Sciences of the United States of America. - 102(2005), 40, Seite 14150-14154
1. Verfasser:	Wu, Wei Biao (VerfasserIn)
Weitere Verfasser:	Rosenblatt, Murray
Format:	Online-Aufsatz
Sprache:	English
Veröffentlicht:	2005
Zugriff auf das übergeordnete Werk:	Proceedings of the National Academy of Sciences of the United States of America
Schlagworte:	Nonlinear time series Limit theory Kernel estimation Weak convergence Mathematics Applied sciences Information science


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245	1	0	\|a Nonlinear System Theory: Another Look at Dependence
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520			\|a 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.
540			\|a Copyright 1993/2005 The National Academy of Sciences of the United States of America
650		4	\|a Nonlinear time series
650		4	\|a Limit theory
650		4	\|a Kernel estimation
650		4	\|a Weak convergence
650		4	\|a Mathematics \|x Pure mathematics \|x Probability theory \|x Random variables \|x Stochastic processes
650		4	\|a Applied sciences \|x Systems science \|x Systems theory
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650		4	\|a Mathematics \|x Pure mathematics \|x Probability theory \|x Stationary processes
650		4	\|a Mathematics \|x Pure mathematics \|x Arithmetic \|x Addition \|x Partial sums
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