Moment-Based Tests under Parameter Uncertainty
提出一类矩变换方法，通过线性修正处理参数不确定性问题，适用于非光滑矩族，并强调稳健矩在检验中的优势，无需依赖估计量；在样本外情形下无需修正。方法应用于风险价值预测的回测。
Abstract This paper considers moment-based tests applied to estimated quantities. We propose a general class of transforms of moments to handle the parameter uncertainty problem. The construction requires only a linear correction that can be implemented in sample and remains valid for some extended families of nonsmooth moments. We reemphasize the attractiveness of working with robust moments, which lead to testing procedures that do not depend on the estimator. Furthermore, no correction is needed when considering the implied test statistic in the out-of-sample case. We apply our methodology to various examples with an emphasis on the backtesting of value-at-risk forecasts.