标题： 正则模型下修正签署似然比统计量的高阶渐近正态性近似 显示英文标题

标题： Higher-order asymptotic normality of approximations to the modified signed likelihood ratio statistic for regular models

摘要： 修正的符号似然比统计量的近似值渐近服从标准正态分布，误差阶数为 $n^{-1}$，其中 $n$ 是样本大小。 这一事实的证明通常需要模型的充分统计量可以写成 $(\hat{\theta},a)$，其中 $\hat{\theta}$ 是模型参数 $\theta$ 的最大似然估计量， 而 $a$ 是一个辅助统计量。 对于许多模型来说，验证这个条件非常困难甚至不可能。 然而，计算这些统计量本身并不需要满足此条件。 本文的目标是给出条件，在无需对模型的充分统计量作任何假设的情况下，使这些统计量渐近正态分布至阶数 $n^{-1}$。 显示英文摘要

摘要： Approximations to the modified signed likelihood ratio statistic are asymptotically standard normal with error of order $n^{-1}$, where $n$ is the sample size. Proofs of this fact generally require that the sufficient statistic of the model be written as $(\hat{\theta},a)$, where $\hat{\theta}$ is the maximum likelihood estimator of the parameter $\theta$ of the model and $a$ is an ancillary statistic. This condition is very difficult or impossible to verify for many models. However, calculation of the statistics themselves does not require this condition. The goal of this paper is to provide conditions under which these statistics are asymptotically normally distributed to order $n^{-1}$ without making any assumption about the sufficient statistic of the model.