负多项与多元正态实验的渐近比较

IF 1.4 3区数学 Q2 STATISTICS & PROBABILITY

Statistica Neerlandica Pub Date : 2023-10-30 DOI:10.1111/stan.12328

Christian Genest, Frédéric Ouimet

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引用次数: 1

摘要

本文提出了负多项概率质量函数与多元正态密度之间的比率的对数的精细局部近似，两者具有相同的均值协方差结构。这个近似是用斯特林公式和对泰勒展开的细致处理推导出来的，它给出了抖动负多项分布和相应的多元正态分布之间的海灵格距离的上界。负多项式和多元正态实验之间的Le Cam距离的上界随之而来。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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 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.

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来源期刊

Statistica Neerlandica 数学-统计学与概率论

CiteScore

2.60

自引率

6.70%

发文量

审稿时长

>12 weeks

期刊介绍： Statistica Neerlandica has been the journal of the Netherlands Society for Statistics and Operations Research since 1946. It covers all areas of statistics, from theoretical to applied, with a special emphasis on mathematical statistics, statistics for the behavioural sciences and biostatistics. This wide scope is reflected by the expertise of the journal’s editors representing these areas. The diverse editorial board is committed to a fast and fair reviewing process, and will judge submissions on quality, correctness, relevance and originality. Statistica Neerlandica encourages transparency and reproducibility, and offers online resources to make data, code, simulation results and other additional materials publicly available.