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Estimating Measures of Sensitivity of Initial Values to Nonlinear Stochastic Systems with Chaos

Jianqing Fan Qiwei Yao Howell Tong

Statistics Theory and Methods mathscidoc:1912.43423

1993
Two measures of sensitivity to initial conditions in nonlinear time series are proposed. The notions give some insight into the relationship between the Fisher information in statistical estimation and initial-value sensitivity in dynamical systems. By using the locally polynomial regression, we develop nonparametric estimates for a conditional density function, its square root and its partial derivatives. The proposed procedures are innovative and of interests in their own right. They are also used to estimate the sensitive measures. The asymptotic normality of the proposed estimators have been proved. We also propose a simple and intuitively appealing method for choosing the bandwidths. Two simulated examples are used as illustrations.
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@inproceedings{jianqing1993estimating,
  title={Estimating Measures of Sensitivity of Initial Values to Nonlinear Stochastic Systems with Chaos},
  author={Jianqing Fan, Qiwei Yao, and Howell Tong},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221114333324117983},
  year={1993},
}
Jianqing Fan, Qiwei Yao, and Howell Tong. Estimating Measures of Sensitivity of Initial Values to Nonlinear Stochastic Systems with Chaos. 1993. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221114333324117983.
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