We characterize the full classes of M-estimators for semiparametric models of general functionals by formally connecting the theory of consistent loss functions from forecast evaluation with the theory of M-estimation. This novel characterization result opens up the possibility for theoretical research on efficient and equivariant M-estimation and, more generally, it allows to leverage existing results on loss functions known from the literature of forecast evaluation in estimation theory.
翻译:我们通过正式将预测评价中连续损失功能理论与M估计理论联系起来,来确定一般功能半参数模型的全类估算员。 这种新颖的定性结果为关于高效和等同估算的理论研究开辟了可能性,更一般地说,它能够利用从预测评价理论文献中了解到的损失功能的现有结果。