Efficiency and Optimality Results for Tests Based on Weighted Rankings
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加权秩检验的效率与最优性结果
- 研究问题
- 在完整区组设计中，仅假设区组内误差可交换时，加权秩检验具有何种渐近分布与效率，怎样选择评分以实现效率最优？
- 方法与思路
- 作者在区组数量趋于无穷时推导原假设及邻近备择下的极限分布，并优化区组内评分、变异度度量和区组间评分函数。
- 材料陈述的贡献
- 摘要称，正态误差且每区组少于八个观测时 Quade 检验比 Friedman 更有效，并分析正态与极值误差下两类秩方法的最优效率。
- 阅读关注点
- 应核对可交换条件与渐近设定、最优性比较的统计量范围，以及区组大小和误差分布如何影响效率结论及评分选择。
- 阅读边界
- 仅据版本未注明的 OpenAlex 索引摘要；效率结果依赖误差分布与区组结构，不能推出任意样本或备择下的普遍功效优势。
原文摘要
The Tukey–Quade method of weighted rankings for the analysis of complete blocks is considered. Assuming only that the within-block error components are exchangeable, the limiting distribution of a large class of test statistics based on this method is obtained under the null hypothesis and under nearby alternatives as the number of blocks increases to infinity. This makes it possible to derive the asymptotic efficiency of the allied tests relative to the maximin most powerful test based on block-location-free statistics. In particular, the Quade test is seen to be more efficient than the Friedman test when there are less than eight observations per block and the errors are assumed to be normally distributed. It is also possible to determine which within-block scores, which measure of block variability, and which between-block score-generating function maximize the asymptotic efficiency. It is seen that the class of test statistics based on the method of weighted rankings compares favorably with the class of test statistics based on the method of unweighted rankings. The intrinsically optimal asymptotic efficiencies of both classes are studied in detail when the errors are normally distributed and when they have the extreme value distribution.