符号检验的一些有限样本性质
Some Finite Sample Properties of the Sign Test
AI总结：
本文证明符号检验在独立非同分布数据下对单双侧假设无偏，并通过反例揭示数据相关性导致过度拒绝，为少聚类环境下的近似随机化检验提供理论洞见。
摘要：
本文包含两个关于符号检验的有限样本结果。首先，我们证明在独立非同分布数据下，符号检验对单侧和双侧假设均是无偏的。双侧情形的证明基于一个新颖的论证，将功效函数的导数与正则二分图联系起来。无偏性随后由此类图上完美匹配的存在性得出。其次，我们提供一个简单的理论反例，表明当数据表现出相关性时，符号检验会过度拒绝。我们的结果有助于理解在少数聚类环境下近似随机化检验的性质。
英文摘要：
This paper contains two finite-sample results concerning the sign test. First, we show that the sign-test is unbiased with independent, non-identically distributed data for both one-sided and two-sided hypotheses. The proof for the two-sided case is based on a novel argument that relates the derivatives of the power function to a regular bipartite graph. Unbiasedness then follows from the existence of perfect matchings on such graphs. Second, we provide a simple theoretical counterexample to show that the sign test over-rejects when the data exhibits correlation. Our results can be useful for understanding the properties of approximate randomization tests in settings with few clusters.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
