Parameter estimation is an important sub-field in statistics and system identification. Various methods for parameter estimation have been proposed in the literature, among which the Two-Stage (TS) approach is particularly promising, due to its ease of implementation and reliable estimates. Among the different statistical frameworks used to derive TS estimators, the min-max framework is attractive due to its mild dependence on prior knowledge about the parameters to be estimated. However, the existing implementation of the minimax TS approach has currently limited applicability, due to its heavy computational load. In this paper, we overcome this difficulty by using a gradient boosting machine (GBM) in the second stage of TS approach. We call the resulting algorithm the Two-Stage Gradient Boosting Machine (TSGBM) estimator. Finally, we test our proposed TSGBM estimator on several numerical examples including models of dynamical systems.

翻译：参数估计是统计学与系统辨识中的重要子领域。文献中已提出多种参数估计方法，其中两阶段（TS）方法因其易于实现且估计结果可靠而颇具前景。在用于推导TS估计量的不同统计框架中，最小-最大框架因对参数先验知识的依赖性较弱而具有吸引力。然而，现有Minimax TS方法的实现因计算负荷较大而适用范围有限。本文通过在两阶段方法的第二阶段引入梯度提升机（GBM）克服这一困难，将所得算法称为两阶段梯度提升机（TSGBM）估计量。最后，我们在包括动态系统模型在内的多个数值算例中验证了所提出的TSGBM估计量。