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摘要翻译：
考虑一个由一个感兴趣的标量参数和一个讨厌的参数向量参数化的模型。关于感兴趣参数的推断可以基于似然比统计量R的符号根。对R的条件分布的标准正态逼近通常具有O(n^{-1/2}）级误差，其中n是样本量。对R作了一些修改，减少了近似中的误差阶数。本文主要研究了Barndorff-Nielsen的修正有向似然比统计量、Severini的经验调整以及DiCiccio和Martin的两个修正，涉及贝叶斯方法和条件似然比统计量。对于每一次修正，采用两种格式来逼近条件累积分布函数；这些是Barndorff-Nielson格式以及Lugannani和Rice格式。所有的近似都应用于两个独立的指数随机变量的均值比的推论。我们构造了单侧和双侧假设检验，并使用检验的实际大小作为准确性的度量来比较这些近似。
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英文标题：
《A comparison of the accuracy of saddlepoint conditional cumulative
distribution function approximations》
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作者：
Juan Zhang, John E. Kolassa
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最新提交年份：
2007
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分类信息：
一级分类：Statistics 统计学
二级分类：Methodology 方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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英文摘要：
Consider a model parameterized by a scalar parameter of interest and a nuisance parameter vector. Inference about the parameter of interest may be based on the signed root of the likelihood ratio statistic R. The standard normal approximation to the conditional distribution of R typically has error of order O(n^{-1/2}), where n is the sample size. There are several modifications for R, which reduce the order of error in the approximations. In this paper, we mainly investigate Barndorff-Nielsen's modified directed likelihood ratio statistic, Severini's empirical adjustment, and DiCiccio and Martin's two modifications, involving the Bayesian approach and the conditional likelihood ratio statistic. For each modification, two formats were employed to approximate the conditional cumulative distribution function; these are Barndorff-Nielson formats and the Lugannani and Rice formats. All approximations were applied to inference on the ratio of means for two independent exponential random variables. We constructed one and two-sided hypotheses tests and used the actual sizes of the tests as the measurements of accuracy to compare those approximations.
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PDF链接：
https://arxiv.org/pdf/708.1069
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