ABSTRACT The paper deals with an asymptotic relative efficiency concept for confidence regions of multidimensional parameters that is based on the expected volumes of the confidence regions. Under standard conditions the asymptotic relative efficiencies of confidence regions are seen to be certain powers of the ratio of the limits of the expected volumes. These limits are explicitly derived for confidence regions associated with certain plugin estimators, likelihood ratio tests and Wald tests. Under regularity conditions, the asymptotic relative efficiency of each of these procedures with respect to each one of its competitors is equal to 1. The results are applied to multivariate normal distributions and multinomial distributions in a fairly general setting.

中文翻译：

---

基于置信区域预期体积的渐近相对效率概念

摘要 本文处理多维参数置信区域的渐近相对效率概念，该概念基于置信区域的预期体积。在标准条件下，置信区域的渐近相对效率被视为预期体积限制比的某些幂。这些限制是为与某些插件估计器、似然比检验和 Wald 检验相关联的置信区域明确导出的。在规律性条件下，这些过程中的每一个相对于其竞争对手的渐近相对效率都等于 1。结果适用于在相当一般的环境中的多元正态分布和多项式分布。