Some Finite Sample Properties of the Sign Test
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arXiv
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866910326729998336 |
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| author | Cai, Yong |
| author_facet | Cai, Yong |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_01412 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Some Finite Sample Properties of the Sign Test Cai, Yong Econometrics 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. |
| title | Some Finite Sample Properties of the Sign Test |
| topic | Econometrics |
| url | https://arxiv.org/abs/2103.01412 |