In this paper, we study application of Le Cam's one‐step method to parameter estimation in ordinary differential equation models. This computationally simple technique can serve as an alternative to numerical evaluation of the popular non‐linear least squares estimator, which typically requires the use of a multistep iterative algorithm and repetitive numerical integration of the ordinary differential equation system. The one‐step method starts from a preliminary n‐consistent estimator of the parameter of interest and next turns it into an asymptotic (as the sample size n→∞) equivalent of the least squares estimator through a numerically straightforward procedure. We demonstrate performance of the one‐step estimator via extensive simulations and real data examples. The method enables the researcher to obtain both point and interval estimates. The preliminary n‐consistent estimator that we use depends on non‐parametric smoothing, and we provide a data‐driven methodology for choosing its tuning parameter and support it by theory. An easy implementation scheme of the one‐step method for practical use is pointed out.

中文翻译：

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一步法在 ODE 模型参数估计中的应用


在本文中，我们研究了 Le Cam 一步法在常微分方程模型参数估计中的应用。这种计算简单的技术可以作为流行的非线性最小二乘估计器数值评估的替代方法，后者通常需要使用多步迭代算法和常微分方程系统的重复数值积分。单步方法从感兴趣参数的初步 n 一致估计量开始，然后通过数值上简单的过程将其转化为最小二乘估计量的渐近（当样本大小 n → 无穷大）等价物。我们通过广泛的模拟和真实数据示例展示了一步估计器的性能。该方法使研究人员能够获得点估计和区间估计。我们使用的初步 n 一致估计器依赖于非参数平滑，并且我们提供了一种数据驱动的方法来选择其调整参数并通过理论支持它。指出了一步法的一种易于实际应用的实现方案。