On the probable error of the ratio of two gamma means
两个伽马总体均值之比的概率误差AI 解读 ↓
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两个伽马总体均值之比的概率误差
- 研究问题
- 对独立伽马样本的总体均值之比，如何构造覆盖率准确且计算可行的置信区间，并与精确检验反演区间比较？
- 方法与思路
- 作者采用参数自助覆盖率校准，利用摘要所述F分布变量的独立性、形状参数估计密度的p*近似和拒绝抽样简化计算。
- 材料陈述的贡献
- 摘要称得到近乎精确的区间，模拟显示其长度与覆盖率接近精确检验反演区间；作者基于实现便利性推荐自助校准。
- 阅读关注点
- 应核对伽马样本的参数设定、独立性结果和密度近似精度，以及校准步骤、模拟设计和所谓近乎精确的评价标准。
- 阅读边界
- 仅据版本未注明的索引摘要，不能把近乎精确理解为严格精确覆盖；参数约束、近似误差界及模拟数值均未提供。
原文摘要
The two-sample Student's t-interval can be derived by parametric bootstrap coverage calibration of the naive, plug-in interval that fails to account for the estimation of the common variance parameter. The same technique results in an essentially exact confidence interval for the ratio of two means based on independent samples from gamma distributions. The gamma problem is more difficult computationally because an exact pivot is not available. However, the computational burden of bootstrap calibration can be reduced to a routine level using the fact that the ratio of sample means is proportional to an exact F-variate that is independent of the conditional maximum likelihood estimator of the shape parameter. The density of the conditional estimator can be approximated with extreme accuracy using the p* formula, and a rejection sampler can be used to simulate from this approximate density. This greatly simplifies bootstrap calibration in this context. An alternative interval is obtained by inverting an exact test described by Jensen (1986). Simulation studies suggest that the two intervals have similar performance in terms of length and coverage. On practice, we recommend the bootstrap calibration method because it is much simpler to implement and is more versatile.