发表机构
University of Michigan（密歇根大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究闭凸集高斯比较不等式，对协方差矩阵有序的中心高斯向量，较小协方差分布赋予特定闭凸集概率至少与较大协方差分布相同，为高斯测度提供单边类似物，还可用于特定统计推断。
AI 中文摘要
我们证明了对于参考概率至少为1/2的闭凸集的高斯比较不等式。对于协方差矩阵在洛纳意义下有序的中心高斯向量，较小协方差分布赋予每个在较大协方差下测度至少为1/2的闭凸集的概率至少与较大协方差分布一样多。这为高斯测度提供了安德森定理的单边类似物。作为统计应用，该结果证明了在显著性水平低于1/2时，对于接受区域为闭凸但不一定对称的检验统计量，使用保守协方差估计器进行单边和序贯受限推断的合理性。
英文摘要
We prove a Gaussian comparison inequality for closed convex sets with reference probability at least 1/2. For centered Gaussian vectors whose covariance matrices are ordered in the Loewner sense, the smaller covariance law assigns at least as much probability as the larger covariance law to every closed convex set with measure at least 1/2 under the larger covariance. More generally, we show that convolving a nondegenerate Gaussian law with any independent centrally symmetric distribution cannot increase the probability of a closed convex set when the convolved probability is at least 1/2. This provides a one-sided analogue of Anderson's Theorem for Gaussian measures. As a statistical application, the result justifies one-sided and order-restricted inference using conservative covariance estimators at significance levels below 1/2 for test statistics whose acceptance regions are closed and convex but not necessarily symmetric.
