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Some Theory of Statistical Inference for Nonlinear Science

William A. Brock and Ehung G. Baek
The Review of Economic Studies
Vol. 58, No. 4 (Jun., 1991), pp. 697-716
Published by: Oxford University Press
Stable URL: http://www.jstor.org/stable/2297828
Page Count: 20
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Some Theory of Statistical Inference for Nonlinear Science
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Abstract

This article shows how standard errors can be estimated for a measure of the number of excited degrees of freedom (the correlation dimension), and a measure of the rate of information creation (a proxy for the Kolmogorov entropy), and a measure of instability. These measures are motivated by nonlinear science and chaos theory. The main analytical method is central limit theory of U-statistics for mixing processes. The paper takes a step toward formal hypothesis testing in nonlinear science and chaos theory.

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