A Unified Approach to Rank Tests for Multivariate and Repeated Measures Designs
多变量与重复测量设计中秩检验的统一方法AI 解读 ↓
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多变量与重复测量设计中秩检验的统一方法
- 研究问题
- 在平衡、完整且每个单元有多次重复的设计中，如何统一构造多变量与重复测量秩检验，同时允许位置和尺度差异？
- 方法与思路
- 作者将全部观测共同排序，以线性秩统计量的二次型构造检验，并在允许位置与尺度变化的局部备择下分析渐近分布。
- 材料陈述的贡献
- 摘要称，该框架涵盖多因素与多变量检验及不要求等相关的重复测量设计，并给出多种秩变换和对齐秩检验的渐近分布。
- 阅读关注点
- 应核对平衡完整设计和重复数要求、共同排序的功效比较条件，以及不同重复测量相关结构下渐近分布的适用范围。
- 阅读边界
- 依据稿件版本未注明的索引摘要；功效提高的具体条件未说明，结果不能直接推广到不平衡或缺失设计，也不能推断刊本变化。
原文摘要
A unified approach to asymptotic rank tests is presented for a wide class of univariate and multivariate models, including repeated measures designs without compound symmetry. The models are assumed to be balanced and complete with more than one replication per cell. The proposed rank tests are constructed by ranking all of the observations together regardless of row, column, or component membership. This method of ranking offers increased power over the method of n-rankings. The resulting test statistic is a quadratic form in linear rank statistics. Asymptotic distributions are determined under Pitman alternatives that allow for both scale and location alternatives. The resulting statistics include tests for factor effects (both scale and location differences) in one-, two-, and higher-way layouts with repeated measures on one or several factors without assuming equicorrelation. Also included are tests for the multivariate two- and k-sample problem, as well as multivariate versions of the tests for multiway layouts and repeated measures designs. For many of the repeated measures designs without equicorrelation, no other rank based statistics have been previously studied. The results also include the asymptotic distributions for many possible rank transform tests for univariate and multivariate models, as well as a rich class of aligned rank tests.