Estimation of Ordinary Differential Equation Parameters Using Constrained Local Polynomial Regression.
Estimation of Ordinary Differential Equation Parameters Using Constrained Local Polynomial Regression.
复制标题
DOI：
10.5705/ss.2012.304
复制
发表时间：
2014-10
影响因子：
1.4
通讯作者：
Wu H
中科院分区：
文献类型：
--
作者：
Ding AA;Wu H
提出了一种新的方法，使用约束局部多项式回归估计常微分方程模型中的未知参数，其目标是改进基于平滑的两阶段伪最小二乘估计。方程的约束条件来自微分方程模型，并被纳入局部多项式回归，以估计微分方程模型中的未知参数。我们还推导出所提出的估计量的渐近偏差和方差。我们的模拟研究表明，我们的新估计是明显优于伪最小二乘估计的估计精度与一个小的代价的计算成本。流感感染的免疫细胞动力学和运输的应用实例进一步说明了所提出的新方法的好处。
We propose a new method to use a constrained local polynomial regression to estimate the unknown parameters in ordinary differential equation models with a goal of improving the smoothing-based two-stage pseudo-least squares estimate. The equation constraints are derived from the differential equation model and are incorporated into the local polynomial regression in order to estimate the unknown parameters in the differential equation model. We also derive the asymptotic bias and variance of the proposed estimator. Our simulation studies show that our new estimator is clearly better than the pseudo-least squares estimator in estimation accuracy with a small price of computational cost. An application example on immune cell kinetics and trafficking for influenza infection further illustrates the benefits of the proposed new method.