Relative error accurate statistic based on nonparametric likelihood
Relative error accurate statistic based on nonparametric likelihood
复制标题
基于非参数似然的相对误差精确统计
DOI：
10.1017/s0266466621000074
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发表时间：
2020
影响因子：
0.8
通讯作者：
Y. Matsushita and T. Otsu
中科院分区：
文献类型：
--
作者：
Camponovo;L.;Y. Matsushita and T. Otsu
本文提出了一种新的由矩条件定义的参数检验统计量，它对尾区概率的近似具有良好的相对误差特性。我们的统计量，称为倾斜指数倾斜（TET）统计量，是通过估计指数倾斜权重下的某些累积生成函数来构造的。我们证明了TET统计量的渐近p值可以提供不可行鞍点统计量的p值的精确逼近，该统计量允许在正态和大偏差区域具有相对顺序误差的Lugannani-Rice型平差。数值结果证明了所提出的TET统计量的准确性。我们的结果涵盖了刚识别和过度识别的矩条件模型。我们分析的一个局限性是，理论近似结果仅适用于不可行的鞍点统计量，而不可行的统计量的p值与可行的TET统计量的p值的接近程度仅在数值上进行评估。
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 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.