Two-sided bounds for PDF’s maximum of a sum of weighted chi-square variables
Two-sided bounds for PDF’s maximum of a sum of weighted chi-square variables
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PDF 加权卡方变量之和的最大值的两侧界限
DOI：
10.1007/978-3-030-83266-7_13
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Ulyanov, V. V.
中科院分区：
文献类型：
--
作者：
Bobkov, S. G.;Naumov, A. A.;Ulyanov, V. V.
为卡方变量加权和的概率密度函数构造两侧界限。考虑中心和非中心卡方变量的两种情况。上限和下限对总和参数具有相同的依赖性，仅在绝对常数上有所不同。获得的估计将非常有用，特别是在比较希尔伯特空间和多维中心极限定理（包括无限维情况）中的两个高斯随机元素时。
Two–sided bounds are constructed for a probability density function of a weighted sum of chi-square variables. Both cases of central and non-central chi-square variables are considered. The upper and lower bounds have the same dependence on the parameters of the sum and differ only in absolute constants. The estimates obtained will be useful, in particular, when comparing two Gaussian random elements in a Hilbert space and in multidimensional central limit theorems, including the infinite-dimensional case.