This paper deals with the Gaussian and bootstrap approximations to the distribution of the max statistic in high dimensions. This statistic takes the form of the maximum over components of the sum of independent random vectors and its distribution plays a key role in many high-dimensional econometric problems. Using a novel iterative randomized Lindeberg method, the paper derives new bounds for the distributional approximation errors. These new bounds substantially improve upon existing ones and simultaneously allow for a larger class of bootstrap methods.

翻译：本文涉及高斯和靴套近似值, 与最高统计的高度分布相近。 该统计的形式是独立随机矢量总和的各个组成部分的最大比值, 其分布在许多高维计量经济学问题中起着关键作用 。 使用新颖的迭代随机Lindeberg 方法, 本文为分布近似错误提供了新的界限 。 这些新界限大大改进了现有的界限, 并同时允许使用更大规模的靴套方法 。