大球概率、高斯比较与反集中
概率论
2018-03-08 v2
摘要
我们推导了希尔伯特空间中两个高斯元素击中一个球的概率之间的 Kolmogorov 距离的非渐近紧界。这些界的关键性质是与维度无关，并且依赖于这些元素的协方差算子之差的核（Schatten-1）范数以及均值偏移的范数。所获得的界显著改进了基于 Pinsker 不等式并通过 Kullback-Leibler 散度得到的界。我们还建立了希尔伯特空间中非中心高斯元素的平方范数的反集中界。本文给出了一系列激励我们结果的例子，以及所获界在统计推断和高维 CLT 中的应用。
引用
@article{arxiv.1708.08663,
title = {Large ball probability, Gaussian comparison and anti-concentration},
author = {Friedrich Götze and Alexey Naumov and Vladimir Spokoiny and Vladimir Ulyanov},
journal= {arXiv preprint arXiv:1708.08663},
year = {2018}
}
备注
27 pages. We have changed the title of the article, since the new one reflects its content much better. The section 2 was almost completely rewritten. Now the main results are much more accurate. We have also rewritten the proves of the main results, made them shorter and easier while the main ideas are the same