Asymptotic scaling laws for precision of parameter estimates in dynamical systems

被引：8

作者：

Horbelt, W ^{[1
]}

Timmer, J ^{[1
]}

机构：

[1] Univ Freiburg, Freiburger Zentrum Datenanalyse & Modellbildung, D-79104 Freiburg, Germany

来源：

PHYSICS LETTERS A | 2003年 / 310卷 / 04期

关键词：

accuracy of parameter estimation; precision of estimates; scaling laws; system identification; differential equation; maximum likelihood;

D O I：

10.1016/S0375-9601(03)00349-9

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

When parameters are estimated from noisy data, the uncertainty of the estimates in terms of their standard deviation typically scales like the inverse square root of the number of data points. In the case of deterministic dynamical systems with added observation noise, superior scaling laws can be achieved. This is demonstrated numerically for the logistic map, the van der Pol oscillator and the Lorenz system, where exponential scaling laws and power laws have been found, depending on the number of degrees of freedom. For some special cases, analytical expressions are derived. (C) 2003 Elsevier Science B.V. All rights reserved.

引用

页码：269 / 280

页数：12

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