TY - JOUR
T1 - Estimation of conditional densities and sensitivity measures in nonlinear dynamical systems
AU - Fan, Jianqing
AU - Yao, Qiwei
AU - Tong, Howell
N1 - Funding Information:
J. Fan's work was partially supported by National Science Foundation Grants and a National Science Foundation Postdoctoral Fellowship. Q. Yao and H. Tong acknowledge partial support of the Science and Engineering Research Council (U.K.). We thank the Editor for concrete suggestions on the restructuring of the paper and for bringing to our attention the reference Blyth (1994). The valuable comments and suggestions from an Associate Editor and a referee are also gratefully acknowledged.
PY - 1996
Y1 - 1996
N2 - 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.
AB - 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.
KW - Conditional density function
KW - Kullback-Leibler information
KW - Locally polynomial regression
KW - Nonlinear time series
KW - Sensitivity to initial values
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U2 - 10.1093/biomet/83.1.189
DO - 10.1093/biomet/83.1.189
M3 - Article
AN - SCOPUS:0001400429
SN - 0006-3444
VL - 83
SP - 189
EP - 206
JO - Biometrika
JF - Biometrika
IS - 1
ER -