Asymptotic comparison of negative multinomial and multivariate normal experiments
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866913296200761344 |
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| author | Genest, Christian Ouimet, Frédéric |
| author_facet | Genest, Christian Ouimet, Frédéric |
| contents | This note presents a refined local approximation for the logarithm of the ratio between the negative multinomial probability mass function and a multivariate normal density, both having the same mean-covariance structure. This approximation, which is derived using Stirling's formula and a meticulous treatment of Taylor expansions, yields an upper bound on the Hellinger distance between the jittered negative multinomial distribution and the corresponding multivariate normal distribution. Upper bounds on the Le Cam distance between negative multinomial and multivariate normal experiments ensue. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_03100 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Asymptotic comparison of negative multinomial and multivariate normal experiments Genest, Christian Ouimet, Frédéric Statistics Theory Probability Computation 62B15, 62E20, 62H10, 62H12 This note presents a refined local approximation for the logarithm of the ratio between the negative multinomial probability mass function and a multivariate normal density, both having the same mean-covariance structure. This approximation, which is derived using Stirling's formula and a meticulous treatment of Taylor expansions, yields an upper bound on the Hellinger distance between the jittered negative multinomial distribution and the corresponding multivariate normal distribution. Upper bounds on the Le Cam distance between negative multinomial and multivariate normal experiments ensue. |
| title | Asymptotic comparison of negative multinomial and multivariate normal experiments |
| topic | Statistics Theory Probability Computation 62B15, 62E20, 62H10, 62H12 |
| url | https://arxiv.org/abs/2308.03100 |