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条件逻辑回归似然分析中的鞍点修正AI 解读

Barndorfi-Nielsen & Cox (1979) introduced the double saddlepoint approximation to the conditional likelihood function for a structural parameter vector given a sufficient statistic for a nuisance parameter vector. This approximation is considered in some detail for the case of multiple logistic regression models with polytomous outcome states. It is shown that the profile score with saddlepoint correction yields a simple derivation of an approximation to the mean of a…

剖面得分函数的Bartlett偏差修正与鞍点修正AI 解读

Bartlett's bias correction to the profile score function is proved equal, to first order, to the leading correction term of the double saddlepoint approximation to the conditional score function in canonical exponential families.

Barndorfi-Nielsen & Cox (1979) introduced the double saddlepoint approximation to the conditional likelihood function for a structural parameter vector given a sufficient statistic for a nuisance parameter vector. This approximation is considered in some detail for the case of multiple logistic regression models with polytomous outcome states. It is shown that the profile score with saddlepoint correction yields a simple derivation of an approximation to the mean of a…

非中心超几何随机变量均值的 Cornfield 近似：若干简易改进AI 解读

This note provides some simple improvements to Cornfield's asymptotic approximation to the mean of a noncentral hypergeometric random variable. Simplicity, in the sense of avoidance of exact computation in favour of easy approximations, derives from an observation of Mantel & Hankey that in a four-fold table with all margins fixed, the ratio of expected cross-products is equal to the odds ratio parameter governing the noncentral distribution of the reference cell. The…

非中心超几何随机变量均值的 Cornfield 近似：若干简便改进AI 解读

This note provides some simple improvements to Cornfield's asymptotic approximation to the mean of a noncentral hypergeometric random variable. Simplicity, in the sense of avoidance of exact computation in favour of easy approximations, derives from an observation of Mantel & Hankey that in a four-fold table with all margins fixed, the ratio of expected cross-products is equal to the odds ratio parameter governing the noncentral distribution of the reference cell. The…

复合多项分布似然函数的单峰性：证明I. J. Good的猜想AI 解读

I. J. Good's 1965 conjecture of the unimodality of the likelihood function of a symmetrical compound multinomial distribution is proved by the variation-diminishing property of the Laplace transform. The result is a special case of a several sample version with asymmetrical compounding Dirichlet distributions. The technique of proof is applied to yield similar results for the negative binomial distribution and a two point mixture of Poissons.