论文标题
效率差距
The Efficiency Gap
论文作者
论文摘要
通过M-和z估计的参数估计在半摩托模型中同样强大，因为通过集成和分化在相应的损失和识别函数之间的一对一关系，一对一功能的估计。对于多元功能，例如多个矩，分位数或对（价值处于风险，预期的不足），该一对一关系失败，而不是每个识别函数都具有抗动力。最重要的含义是效率差距：最有效的Z估计器通常优于最有效的M估计器。从理论上讲，我们为在不同级别和对（价值处于风险，预期短缺）的多个分位数中建立了这种现象，并以数值为单位说明了差距。我们的结果进一步为伪有效的M估计性提供了指导，以实现风险和预期短缺的价值的半参数模型。
Parameter estimation via M- and Z-estimation is equally powerful in semiparametric models for one-dimensional functionals due to a one-to-one relation between corresponding loss and identification functions via integration and differentiation. For multivariate functionals such as multiple moments, quantiles, or the pair (Value at Risk, Expected Shortfall), this one-to-one relation fails and not every identification function possesses an antiderivative. The most important implication is an efficiency gap: The most efficient Z-estimator often outperforms the most efficient M-estimator. We theoretically establish this phenomenon for multiple quantiles at different levels and for the pair (Value at Risk, Expected Shortfall), and illustrate the gap numerically. Our results further give guidance for pseudo-efficient M-estimation for semiparametric models of the Value at Risk and Expected Shortfall.
