Contrasts under Long-Range Correlations
长程相关下的对比统计量AI 解读 ↓
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长程相关下的对比统计量
- 研究问题
- 当观测存在长程相关时，实验条件之间的对比统计量，其检验水平、置信区间、功效与估计效率会受到怎样的影响？
- 方法与思路
- 作者研究随机化使实验条件充分混合时的对比推断，并提出无需估计相关结构的简单分块方法，以减少功效和效率损失。
- 材料陈述的贡献
- 摘要称，充分随机混合可维持独立性假设下推断的渐近有效性，但仍有明显功效与效率损失，分块可大幅缓解。
- 阅读关注点
- 核对对比统计量的定义、长程依赖与随机混合的具体条件，以及分块方式、渐近论证和有限样本近似的适用范围。
- 阅读边界
- 仅据 OpenAlex 索引摘要，稿件版本未注明；依赖条件及分块细节未说明，不能把有效性结论推广到任意设计或推断程序。
原文摘要
The background of the paper is the empirical observation from a variety of subject areas that long-range correlations appear to be much more frequent than has been previously assumed. This includes high-quality measurement series which are commonly treated as prototypes of "i.i.d." observations. Evidence is briefly cited in the paper. It has already been shown elsewhere that long-range dependence leads to results that can be qualitatively different from those obtained under short-range dependence, and in particular, that long-range dependence has drastic effects on the naive statistical treatment of absolute constants. The natural question arising from this, also of relevance for statistical practice, is how the long-range dependence affects the statistics for contrasts. The main answer given in this paper is twofold. (i) If the experimental conditions are well mixed as provided by randomization, the levels of tests and confidence intervals derived under the independence assumption are still correct, asymptotically and usually in good approximation for finite samples. (ii) Even under randomly mixed designs there are typically large unnoticed power and efficiency losses due to the long-range dependence. They can be greatly reduced without estimating the correlations by a simple blocking device.