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Non-uniform Berry-Esseen Bounds for Coordinate Symmetric Random Vectors with Applications

$icon-email$ Le Van Thanh , Nguyen Ngoc Tu

Abstract

This work establishes the nonuniform Berry-Esseen inequality for coordinate symmetric vectors. The nonuniform $L_{p}$ $(p \geq 1)$ bound is also established. The main results are applied to projections of random vectors distributed according to a family of measures on the $ℓ_{r}^{n}$ sphere and the $ℓ_{r}^{n}$ ball, including cone measure and volume measure.

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Non-uniform Berry-Esseen Bounds for Coordinate Symmetric Random Vectors with Applications

Abstract