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.

中文翻译：

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使用约束局部多项式回归估计常微分方程参数

我们提出了一种新方法，使用约束局部多项式回归来估计常微分方程模型中的未知参数，目的是改进基于平滑的两阶段伪最小二乘估计。方程约束来自微分方程模型，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。我们还推导出了所提出的估计量的渐近偏差和方差。我们的模拟研究表明，我们的新估计器在估计精度方面明显优于伪最小二乘估计器，而且计算成本很小。关于流感感染的免疫细胞动力学和贩运的应用示例进一步说明了所提出的新方法的好处。