Estimation of conditional densities and sensitivity measures in nonlinear dynamical systems

Jianqing Fan, Qiwei Yao, Howell Tong

Research output: Contribution to journalArticlepeer-review

206 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)189-206
Number of pages18
Issue number1
StatePublished - 1996
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • General Mathematics
  • Agricultural and Biological Sciences (miscellaneous)
  • General Agricultural and Biological Sciences
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


  • Conditional density function
  • Kullback-Leibler information
  • Locally polynomial regression
  • Nonlinear time series
  • Sensitivity to initial values


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