$\sqrt{n}$ -常微分方程系统的一致参数估计：通过平滑绕过数值积分
$\sqrt{n}$-consistent parameter estimation for systems of ordinary differential equations: bypassing numerical integration via smoothing
摘要：
本文研究了一个常微分方程系统的参数估计问题。在系统是非线性的情况下，正如在实际应用中通常是的那样，它的分析解通常不存在。因此，简单的估计方法，如普通的最小二乘法依赖于重复使用数值积分，以确定所考虑的每个参数值的系统的解决方案，并随后找到最小化目标函数的参数估计。这对这种估计方法引起巨大的计算负荷。我们研究的一致性的替代估计，被定义为一个最小的适当的距离之间的nonparametrically估计的衍生物的解决方案和右手边的系统应用到一个nonparametrically估计的解决方案。与普通最小二乘法相比，这种平滑和匹配估计器（SME）完全绕过了数值积分，大大减少了计算时间。此外，我们表明，在适当的正则性条件下，这种光滑和匹配的估计过程导致一个$\sqrt{n}$一致的估计参数的兴趣。
英文摘要：
We consider the problem of parameter estimation for a system of ordinary differential equations from noisy observations on a solution of the system. In case the system is nonlinear, as it typically is in practical applications, an analytic solution to it usually does not exist. Consequently, straightforward estimation methods like the ordinary least squares method depend on repetitive use of numerical integration in order to determine the solution of the system for each of the parameter values considered, and to find subsequently the parameter estimate that minimises the objective function. This induces a huge computational load to such estimation methods. We study the consistency of an alternative estimator that is defined as a minimiser of an appropriate distance between a nonparametrically estimated derivative of the solution and the right-hand side of the system applied to a nonparametrically estimated solution. This smooth and match estimator (SME) bypasses numerical integration altogether and reduces the amount of computational time drastically compared to ordinary least squares. Moreover, we show that under suitable regularity conditions this smooth and match estimation procedure leads to a $\sqrt{n}$-consistent estimator of the parameter of interest.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
