Estimation of conditional densities and sensitivity measures in nonlinear dynamical systems

Jianqing Fan; Qiwei Yao; Howell Tong

doi:10.1093/biomet/83.1.189

Estimation of conditional densities and sensitivity measures in nonlinear dynamical systems

Jianqing Fan
, Qiwei Yao
, Howell Tong

Research output: Contribution to journal › Article › peer-review

226 Scopus citations

Abstract

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 language	English (US)
Pages (from-to)	189-206
Number of pages	18
Journal	Biometrika
Volume	83
Issue number	1
DOIs	https://doi.org/10.1093/biomet/83.1.189
State	Published - 1996
Externally published	Yes

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

Keywords

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

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10.1093/biomet/83.1.189

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title = "Estimation of conditional densities and sensitivity measures in nonlinear dynamical systems",

abstract = "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.",

keywords = "Conditional density function, Kullback-Leibler information, Locally polynomial regression, Nonlinear time series, Sensitivity to initial values",

author = "Jianqing Fan and Qiwei Yao and Howell Tong",

note = "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.",

year = "1996",

doi = "10.1093/biomet/83.1.189",

language = "English (US)",

volume = "83",

pages = "189--206",

journal = "Biometrika",

issn = "0006-3444",

publisher = "Oxford University Press",

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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 -

Estimation of conditional densities and sensitivity measures in nonlinear dynamical systems

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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