In this paper, we derive new, nearly optimal bounds for the Gaussian approximation to scaled averages of n independent high-dimensional centered random vectors X1,…,Xn over class rectangles in case when covariance matrix average is nondegenerate. bounded Xi’s, implied bound Kolmogorov distance between distribution and vector takes form C(Bn2log3d/n)1/2logn, where d dimension Bn a uniform envelo...