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Estimation of conditional densities and sensitivity measures in nonlinear dynamical systems

Jianqing Fan Qiwei Yao Howell Tong

Statistics Theory and Methods mathscidoc:1912.43270

Biometrika, 83, (1), 189-206, 1996.3
Using locally polynomial regression, we develop nonparametric estimators for the conditional density function and its square root, and their partial derivatives. Two measures of sensitivity to initial conditions in nonlinear stochastic dynamic systems are proposed, one of which relates Fisher information with initial-value sensitivity in dynamical systems. We propose estimators for these, and show asymptotic normality for one of them. We further propose a simple method for choosing the bandwidth. The methods are illustrated by simulation of two well-known models in dynamical systems.
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@inproceedings{jianqing1996estimation,
  title={Estimation of conditional densities and sensitivity measures in nonlinear dynamical systems},
  author={Jianqing Fan, Qiwei Yao, and Howell Tong},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113407855583830},
  booktitle={Biometrika},
  volume={83},
  number={1},
  pages={189-206},
  year={1996},
}
Jianqing Fan, Qiwei Yao, and Howell Tong. Estimation of conditional densities and sensitivity measures in nonlinear dynamical systems. 1996. Vol. 83. In Biometrika. pp.189-206. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113407855583830.
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