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Biometrika 1996 83(1):189-206; doi:10.1093/biomet/83.1.189
© 1996 by Biometrika Trust
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Estimation of conditional densities and sensitivity measures in nonlinear dynamical systems

JIANQING FAN, QIWEI YAO and HOWELL TONG

Department of Statistics, University of North Carolina Chapel Hill, North Carolina 27599-3260, U.S.A.
Institute of Mathematics and Statistics, University of Kent Canterbury, Kent CT2 7NF, U.K.

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.

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


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