Modified Large-Sample Confidence Intervals for Linear Combinations of Variance Components
方差分量线性组合的修正大样本置信区间AI 解读 ↓
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方差分量线性组合的修正大样本置信区间
- 研究问题
- 当多元正态模型的方差分量估计量相互依赖时，如何构造其线性组合的置信区间或置信界，并评估覆盖误差？
- 方法与思路
- 作者利用正态向量二次型的卡方表示扩展 MLS 方法，并通过 Edgeworth 与 Cornish–Fisher 展开推导二阶覆盖误差。
- 材料陈述的贡献
- 摘要称，MLS 置信界一般不具二阶准确性，但可构造二阶准确的版本；文章还讨论总体生物等效性应用与模拟。
- 阅读关注点
- 应核对依赖结构如何进入 MLS 构造、二阶修正所需条件，以及与正态近似比较和生物等效性示例的适用范围。
- 阅读边界
- 仅据版本未注明的 OpenAlex 索引摘要；覆盖误差公式、特殊情形和模拟数值未提供，所述优于正态近似的结论须核对全文。
原文摘要
We consider the problem of setting a confidence interval or bound for a linear combination of variance components related to a multivariate normal distribution, which includes important applications such as comparing variance components and testing the bioequivalence between two drug products. The lack of an exact confidence interval for a general linear combination of variance components spurred the development of a modified large-sample (MLS) method that was shown to be superior to many other approximation methods. But existing MLS method requires the use of independent estimators of variance components. Using a chi-squared representation of a quadratic form of a multivariate normal vector, we extend the MLS method to situations in which estimators of variance components are dependent. Using Edgeworth and Cornish–Fisher expansions, we explicitly derive the second-order asymptotic coverage error of the MLS confidence bound. Our results show that the MLS confidence bound is not second-order accurate in general, but is much better than the confidence bound based on normal approximation and is nearly second-order accurate in some special cases. Our results also show how to construct an MLS confidence bound that is second-order accurate. As an application, we discuss the use of the MLS method in assessing population bioequivalence, with some simulation results and an example.