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Non-uniform Berry-Esseen Bounds for Coordinate Symmetric Random Vectors with Applications
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 ${\ell _{r}^{n}}$ sphere and the ${\ell _{r}^{n}}$ ball, including cone measure and volume measure.