Asymptotic comparison of negative multinomial and multivariate normal experiments
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 metic...
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| Veröffentlicht in: | Statistica Neerlandica 2024-05, Vol.78 (2), p.427-440 |
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| container_title | Statistica Neerlandica |
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| creator | Genest, Christian Ouimet, Frédéric |
| description | 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. |
| doi_str_mv | 10.1111/stan.12328 |
| format | Article |
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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. 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| language | eng |
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| source | Wiley Online Library Journals Frontfile Complete |
| subjects | Approximation asymptotic theory comparison of experiments Le Cam distance local limit theorem Mathematical analysis Multivariate analysis multivariate normal distribution negative multinomial distribution Normal distribution Statistical analysis Upper bounds |
| title | Asymptotic comparison of negative multinomial and multivariate normal experiments |
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