RELATIVE ERROR ACCURATE STATISTIC BASED ON NONPARAMETRIC LIKELIHOOD
提出一种新的检验统计量（倾斜指数倾斜统计量），通过估计指数倾斜权重下的累积生成函数，在尾部概率近似中实现相对误差阶为n^{-1}的精确性，适用于恰好识别和过度识别的矩条件模型。
This paper develops a new test statistic for parameters defined by moment conditions that exhibits desirable relative error properties for the approximation of tail area probabilities. Our statistic, called the tilted exponential tilting (TET) statistic, is constructed by estimating certain cumulant generating functions under exponential tilting weights. We show that the asymptotic p -value of the TET statistic can provide an accurate approximation to the p -value of an infeasible saddlepoint statistic, which admits a Lugannani–Rice style adjustment with relative errors of order $n^{-1}$ both in normal and large deviation regions. Numerical results illustrate the accuracy of the proposed TET statistic. Our results cover both just- and overidentified moment condition models. A limitation of our analysis is that the theoretical approximation results are exclusively for the infeasible saddlepoint statistic, and closeness of the p -values for the infeasible statistic to the ones for the feasible TET statistic is only numerically assessed.