In this article, we study the critical growth rates of dimension below which Gaussian critical values can be used for hypothesis testing but beyond which they cannot. We are particularly interested in how these growth rates depend on the number of moments that the observations possess.

翻译：本文研究了维数的临界增长速度：低于该速度时高斯临界值可用于假设检验，而超过该速度则不能。我们特别关注这些增长速度如何依赖于观测数据所拥有的矩的个数。