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Chain rules for multivariate cumulant coefficients
Stat ( IF 1.7 ) Pub Date : 2022-01-06 , DOI: 10.1002/sta4.451
Christopher S. Withers 1 , Saralees Nadarajah 2
Affiliation  

Cumulant coefficients are the building blocks of Edgeworth expansions and other analytic methods for statistical inference, such as bias reduction. Suppose that w^ is a standard estimate of an unknown vector w and that t(·) is a smooth function on w. We show that t^=tw^ is a standard estimate of t(w). We give its cumulant coefficients in terms of those of w^ and the derivatives of t(w). These “chain rules” can then be used to get the cumulant coefficients of a smooth function of t^. The results are illustrated by two numerical examples.

中文翻译:

多元累积系数的链式法则

累积系数是 Edgeworth 展开和其他统计推断分析方法(例如减少偏差)的构建块。假设 w ̂ 是未知向量 w 的标准估计,t(·) 是 w 上的平滑函数。我们表明 ̂ = t ( w ̂ ) 是 t(w) 的标准估计值。我们给出它的累积系数 w ̂ 以及 t(w) 的导数。然后可以使用这些“链式规则”来获得平滑函数的累积系数 ̂ . 结果通过两个数值例子来说明。
更新日期:2022-01-06
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