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We derive a Gaussian approximation result for the maximum of a sum of randomvectors under $(2+\iota)$-th moments. Our main theorem is abstract andnonasymptotic, and can be applied to a variety of statistical learningproblems. The proof uses the Lindeberg telescopic sum device along with someother newly developed technical results.

Gaussian Approximations for Maxima of Random Vectors under $(2+\iota)$-th Moments