Gaussian Approximations for Maxima of Random Vectors under (2+ι)-th Moments

05/27/2019

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by   Qiang Sun, et al.

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We derive a Gaussian approximation result for the maximum of a sum of random vectors under (2+ι)-th moments. Our main theorem is abstract and nonasymptotic, and can be applied to a variety of statistical learning problems. The proof uses the Lindeberg telescopic sum device along with some other newly developed technical results.