Parameter estimation of ODE's via nonparametric estimators
Parameter estimation of ODE's via nonparametric estimators
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DOI：
10.1214/07-ejs132
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发表时间：
2008-01-01
影响因子：
1.1
通讯作者：
Brunel, Nicolas J-B.
中科院分区：
文献类型：
--
作者：
Brunel, Nicolas J-B.
常微分方程（ODE）是物理学、化学和生物学中广泛应用的模型。特别是，这种数学形式主义用于描述复杂系统的演化，它可能包括高维耦合非线性微分方程组。在这种情况下，我们提出了一个一般的方法估计指标OD E的时间序列的参数。我们的方法能够减轻经典参数方法所遇到的计算困难。这些困难是由于模型的隐含定义。我们建议使用的回归函数的非参数估计作为第一步在建设一个M-估计，我们显示的一致性，在一般条件下导出的估计。在样条估计的情况下，我们证明了渐近正态性，收敛速度是通常的根n-率参数估计。一些观点的改进，这个新的家庭的参数估计。
Ordinary differential equations (ODE's) are widespread models in physics, chemistry and biology. In particular, this mathematical formalism is used for describing the evolution of complex systems and it might consist of high-dimensional sets of coupled nonlinear differential equations. In this setting, we propose a general method for estimating the parameters indexing OD E's from times series. Our method is able to alleviate the computational difficulties encountered by the classical parametric met hods. These difficulties are due to the implicit definition of the model. We propose the use of a nonparametric estimator of regression functions as a first-step in the construction of an M-estimator, and we show the consistency of the derived estimator under general conditions. In the case of spline estimators, we prove asymptotic normality, and that the rate of convergence is the usual root n-rate for parametric estimators. Some perspectives of refinements of this new family of parametric estimators are given.