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摘要翻译：
常微分方程是物理、化学和生物学中广泛应用的模型。特别是，这种数学形式用于描述复杂系统的演化，它可能由高维耦合非线性微分方程组组成。在此背景下，我们提出了一种从时间序列中估计参数索引ODE的一般方法。我们的方法可以减轻经典参数化方法所遇到的计算困难。这些困难是由于模型的隐式定义。我们提出利用回归函数的非参数估计作为构造M-估计的第一步，并在一般条件下证明了所导出估计的相合性。在样条估计的情况下，我们证明了渐近正态性，并且证明了参数估计的收敛速度是通常的$\sqrt{n}$-速度。给出了这一新的参数估计族的改进的一些观点。
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英文标题：
《Parameter estimation of ODE's via nonparametric estimators》
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作者：
Nicolas J-B. Brunel
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最新提交年份：
2008
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分类信息：
一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
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 ODE's from times series. Our method is able to alleviate the computational difficulties encountered by the classical parametric methods. 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 $\sqrt{n}$-rate for parametric estimators. Some perspectives of refinements of this new family of parametric estimators are given.
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PDF链接：
https://arxiv.org/pdf/710.419
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