On Multivariate Runs Tests for Randomness
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多变量随机性的游程检验
- 研究问题
- 研究如何将游程概念推广到多变量观测，以检验序列是否存在依赖，并在异方差及缺乏矩条件的情形下保持稳健性。
- 方法与思路
- 作者定义椭圆型与矩阵值游程，构造仿射不变检验，推导零假设及局部向量 ARMA 备择下的极限分布并开展模拟。
- 材料陈述的贡献
- 摘要称矩阵值游程检验在中高维比较中表现良好，并揭示另一类游程检验的一致性问题；两类检验结合可能帮助理解拒绝原因。
- 阅读关注点
- 应核对随机性零假设的具体含义、允许的异方差形式、局部备择与效率比较条件，以及一致性问题出现的依赖结构。
- 阅读边界
- 依据版本未注明的 OpenAlex 索引摘要；未给出完整理论条件与比较范围，不能将稳健性或效率结论无限外推或推断刊本变化。
原文摘要
This paper proposes several extensions of the concept of runs to the multivariate setup, and studies the resulting tests of multivariate randomness against serial dependence. Two types of multivariate runs are defined: (i) an elliptical extension of the spherical runs proposed by Marden (1999), and (ii) an original concept of matrix-valued runs. The resulting runs tests themselves exist in various versions, one of which is a function of the number of data-based hyperplanes separating pairs of observations only. All proposed multivariate runs tests are affine-invariant and highly robust: in particular, they allow for heteroscedasticity and do not require any moment assumption. Their limiting distributions are derived under the null hypothesis and under sequences of local vector ARMA alternatives. Asymptotic relative efficiencies with respect to Gaussian Portmanteau tests are computed, and show that, while Marden-type runs tests suffer severe consistency problems, tests based on matrix-valued runs perform uniformly well for moderate-to-large dimensions. A Monte Carlo study confirms the theoretical results and investigates the robustness properties of the proposed procedures. A real-data example is also treated, and shows that combining both types of runs tests may provide some insight on the reason why rejection occurs, hence that Marden-type runs tests, despite their lack of consistency, also are of interest for practical purposes.