Gaussian approximations for maxima of random vectors under (2+ι)-th moments

Strong Gaussian Approximation for the Sum of Random Vectors

“…Gaussian approximation of the maximum function is very useful for justifying the Bootstrap validity and for approximating the distributions with different statistics in high-dimensional models. Besides, the aforementioned papers [8,9], some relevant results can also be found in works [18] and [23], where the authors rely on Malliavin calculus and high-order moments to assess the corresponding bounds. In [15], the authors go after the same approximation as reported herein; however, using a completely different tool: the Stein method instead of the Wasserstein distance, yielding a result that is only valid under the constraint that the measure of i.i.d.…”