论文标题
高斯措施移动的确切下限和上限
Exact lower and upper bounds for shifts of Gaussian measures
论文作者
论文摘要
确切的上限和下限是$ \ MATHSF {E} W（\ MathBf {X} - \ MathBf {V}）/\ Mathsf {E} W（\ Mathbf {X}）$，用于中心的高斯随机vector $ \ MathBf { of $\mathsf{E}w(\mathbf{X}-t\mathbf{v})$ in $t$, where $w\colon\mathbb{R}^n\to[0,\infty)$ is any even unimodal function and $\mathbf{v}$ is any vector in $\mathbb{R}^n$.作为这种结果的推论，给出了多元正态分布平均值的统计测试功率函数的精确上限和下限。
Exact upper and lower bounds on the ratio $\mathsf{E}w(\mathbf{X}-\mathbf{v})/\mathsf{E}w(\mathbf{X})$ for a centered Gaussian random vector $\mathbf{X}$ in $\mathbb{R}^n$, as well as bounds on the rate of change of $\mathsf{E}w(\mathbf{X}-t\mathbf{v})$ in $t$, where $w\colon\mathbb{R}^n\to[0,\infty)$ is any even unimodal function and $\mathbf{v}$ is any vector in $\mathbb{R}^n$. As a corollary of such results, exact upper and lower bounds on the power function of statistical tests for the mean of a multivariate normal distribution are given.
