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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | https://arxiv.org/abs/2404.13248 |
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| _version_ | 1866916215092412416 |
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| author | Perlman, Michael D. |
| author_facet | Perlman, Michael D. |
| contents | A {\it pure significance test} (PST) tests a simple null hypothesis $H_f:Y\sim f$ {\it without specifying an alternative hypothesis} by rejecting $H_f$ for {\it small} values of $f(Y)$. When the sample space supports a proper uniform pmf $f_\mathrm{unif}$, the PST can be viewed as a classical likelihood ratio test for testing $H_f$ against this uniform alternative. Under this interpretation, standard test features such as power, Kullback-Leibler divergence, and expected $p$-value can be considered. This report focuses on PSTs for multinomial and binomial distributions, and for the related goodness-of-fit testing problems with the uniform alternative. The case of repeated observations cannot be reduced to the single observation case via sufficiency. The {\it ordered binomial distribution}, apparently new, arises in the course of this study. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_13248 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Pure Significance Tests for Multinomial and Binomial Distributions: the Uniform Alternative Perlman, Michael D. Statistics Theory 62F03 (Primary) A {\it pure significance test} (PST) tests a simple null hypothesis $H_f:Y\sim f$ {\it without specifying an alternative hypothesis} by rejecting $H_f$ for {\it small} values of $f(Y)$. When the sample space supports a proper uniform pmf $f_\mathrm{unif}$, the PST can be viewed as a classical likelihood ratio test for testing $H_f$ against this uniform alternative. Under this interpretation, standard test features such as power, Kullback-Leibler divergence, and expected $p$-value can be considered. This report focuses on PSTs for multinomial and binomial distributions, and for the related goodness-of-fit testing problems with the uniform alternative. The case of repeated observations cannot be reduced to the single observation case via sufficiency. The {\it ordered binomial distribution}, apparently new, arises in the course of this study. |
| title | Pure Significance Tests for Multinomial and Binomial Distributions: the Uniform Alternative |
| topic | Statistics Theory 62F03 (Primary) |
| url | https://arxiv.org/abs/2404.13248 |