The asymptotic distribution and Berry--Esseen bound of a new test for independence in high dimension with an application to stochastic optimization

Wei-Dong Liu, Zhengyan Lin, Qi-Man Shao

Let ${\mathbf{X}}_1,...,{\mathbf{X}}_n$ be a random sample from a $p$-dimensional population distribution. Assume that $c_1{n}^{\alpha }\le p\le c_2{n}^{\alpha }$ for some positive constants $c_1,c_2$ a…