发表机构
LIDAM, UCLouvain; Département de mathématiques, Université libre de Bruxelles; Vrije Universiteit Brussel（卢旺天主教大学 LIDAM; 布鲁塞尔自由大学数学系; 布鲁塞尔自由大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文为Satterthwaite近似推导显式Gamma-Stein界，通过核表示和矩匹配控制近似误差，应用于方差估计与高维统计。
AI 中文摘要
我们为独立卡方随机变量加权和（更一般地，独立Gamma随机变量的加权和）的Satterthwaite近似推导了显式的Gamma-Stein界。近似Gamma分布通过匹配前两阶矩来选取。我们的方法依赖于Gamma-Stein方程解及其在正实数轴上的一阶导数的新核表示。这些表示产生了适应矩匹配结构的加权Stein因子界，并表明近似的质量直接由各个尺度参数与匹配尺度参数之间的差异控制。通过平滑处理获得Kolmogorov界。这些结果为广泛使用的Satterthwaite近似提供了定量保证，并应用于合并方差、平稳高斯时间序列的样本方差、Wishart迹及Wishart迹之和，以及高维重复测量统计。
英文摘要
We derive explicit Gamma--Stein bounds for the Satterthwaite approximation of weighted sums of independent chi-square random variables and, more generally, of independent Gamma random variables. The approximating Gamma distribution is chosen by matching the first two moments. Our approach relies on new kernel representations of the solution to the Gamma--Stein equation and of its first derivatives on the positive real line. These representations yield weighted Stein-factor bounds adapted to the moment-matching structure and show that the quality of the approximation is controlled directly by the discrepancies between the individual scale parameters and the matched scale parameter. Kolmogorov bounds are obtained by smoothing. The results provide quantitative guarantees for the widely used Satterthwaite approximation and are applied to pooled variances, sample variances of stationary Gaussian time series, Wishart traces and sums of Wishart traces, and high-dimensional repeated-measures statistics.
Comments27 pages, 2 figures
