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

Abstract

This work establishes the nonuniform Berry-Esseen inequality for coordinate symmetric vectors. The nonuniform Lp (p ≥\u20091) bound is also established. The main results are applied to projections of random vectors distributed according to a family of measures on the ℓrn${\\ell _{r}^{n}}$ sphere and the ℓrn${\\ell _{r}^{n}}$ ball, including cone measure and volume measure.