具有任意小偏度的矩阵
Pivotal Quantities with Arbitrary Small Skewness
摘要：
在本文中，我们提出了随机化的方法，以提高中心极限定理（CLT）的人口平均值$μ$的推断的准确性。我们介绍了一个广泛的学生$t$ -统计量，经典的枢轴$μ$，继续拥有枢轴属性$μ$和他们的偏度可以任意小，每个固定的样本量$n$的随机版本。因此，这些随机化的枢轴承认CLT具有较小的误差。本文中的随机化框架还提供了一个显式的CLT的精度之间的关系，随机枢轴和其相关的置信区域的体积为单变量和多变量数据的平均值。该属性允许调节本文中讨论的随机化置信区域的准确性和体积之间的权衡。
英文摘要：
In this paper we present randomization methods to enhance the accuracy of the central limit theorem (CLT) based inferences about the population mean $μ$. We introduce a broad class of randomized versions of the Student $t$-statistic, the classical pivot for $μ$, that continue to possess the pivotal property for $μ$ and their skewness can be made arbitrarily small, for each fixed sample size $n$. Consequently, these randomized pivots admit CLTs with smaller errors. The randomization framework in this paper also provides an explicit relation between the precision of the CLTs for the randomized pivots and the volume of their associated confidence regions for the mean for both univariate and multivariate data. This property allows regulating the trade-off between the accuracy and the volume of the randomized confidence regions discussed in this paper.
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