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Some Finite Sample Properties of the Sign Test

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  • Yong Cai

Abstract

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.

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  • Yong Cai, 2021. "Some Finite Sample Properties of the Sign Test," Papers 2103.01412, arXiv.org, revised Feb 2024.
    • Handle: RePEc:arx:papers:2103.01412
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    References listed on IDEAS

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