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Asymptotic comparison of negative multinomial and multivariate normal experiments

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  • Christian Genest
  • Frédéric Ouimet

Abstract

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.

Suggested Citation

  • Christian Genest & Frédéric Ouimet, 2024. "Asymptotic comparison of negative multinomial and multivariate normal experiments," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 78(2), pages 427-440, May.
    • Handle: RePEc:bla:stanee:v:78:y:2024:i:2:p:427-440
    DOI: 10.1111/stan.12328
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    References listed on IDEAS

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    1. Sagae, Masahiko & Tanabe, Kunio, 1992. "Symbolic Cholesky decomposition of the variance--covariance matrix of the negative multinomial distribution," Statistics & Probability Letters, Elsevier, vol. 15(2), pages 103-108, September.
    2. Frédéric Ouimet, 2023. "A refined continuity correction for the negative binomial distribution and asymptotics of the median," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(7), pages 827-849, October.
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