Many processes in biology, chemistry, physics, medicine, and engineering aremodeled by a system of differential equations. Such a system is usuallycharacterized via unknown parameters and estimating their 'true' value is thusrequired. In this paper we focus on the quite common systems for which thederivatives of the states may be written as sums of products of a function ofthe states and a function of the parameters. For such a system linear in functions of the unknown parameters we present anecessary and sufficient condition for identifiability of the parameters. Wedevelop an estimation approach that bypasses the heavy computational burden ofnumerical integration and avoids the estimation of system states derivatives,drawbacks from which many classic estimation methods suffer. We also suggest anexperimental design for which smoothing can be circumvented. The optimal rateof the proposed estimators, i.e., their $\sqrt n$-consistency, is proved andsimulation results illustrate their excellent finite sample performance andcompare it to other estimation approaches.
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机译：生物学，化学，物理学，医学和工程学中的许多过程都是由微分方程组建模的。这样的系统通常通过未知参数来表征，因此需要估计它们的“真实”值。在本文中，我们关注于非常常见的系统，对于这些系统，状态的导数可以写为状态函数与参数函数的乘积之和。对于这样一个线性系统，它具有未知参数的函数，我们为参数的可辨识性提供了充要条件。我们开发了一种估计方法，该方法绕开了数值积分的繁重计算负担，并且避免了许多经典估计方法所遭受的系统状态导数，缺点的估计。我们还建议可以避免平滑的实验设计。证明了所提出的估计量的最优速率，即它们的$ \ sqrt n $-一致性，并且仿真结果说明了它们出色的有限样本性能并将其与其他估计方法进行比较。
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