Nonparametric estimation of nonlinear dynamics by metric-based local linear approximation
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This paper discusses nonparametric estimation of nonlinear dynamical system models by a method of metric-based local linear approximation. We assume no functional form of a given model but estimate it from experimental data by approximating the curve implied by the function by the tangent plane around the neighborhood of a tangent point. To specify an appropriate neighborhood, we prepare a metric defined over the Euclidean space in which the curve exists and then evaluate the closeness to the tangent point according to the distances. The proposed method differs from the first order polynomial modeling in discerning the metric and the weighting function, but the first order polynomial modeling with Gaussian kernels is shown to be a special version of the proposed method. Simulation studies and application to ECG signals show the proposed method is easy to manipulate and has performance comparable to or better than the first order local polynomial modeling.
KeywordsElectrocardiogram Local linear approximation Nonlinear dynamical system Nonparametric estimation Random oscillation
We are grateful to the editor, anonymous referees and Dr. Hirokazu Yanagihara for their helpful comments and suggestions.
- Fan J, Gijbels I (1996) Local polynomial modeling and its applications. Chapman and Hall, LondonGoogle Scholar
- Fan J, Yao QW (2005) Nonlinear time series: nonparametric and parametric methods. Springer, BerlinGoogle Scholar
- Izhikevich EM (2010) Dynamical systems in neuroscience: the geometry of excitability and bursting. The MIT Press, CambridgeGoogle Scholar
- Strogatz SH (1994) Nonlinear dynamics and chaos. Westview Press, BoulderGoogle Scholar
- Wasserman L (2006) All of nonparametric statistics. SpringerGoogle Scholar