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 ≥ 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.

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Acknowledgements

The authors are grateful to the referee for carefully reading of the manuscript and for offering comments which enabled them to substantially improve the paper.

Funding

The paper was supported by National Foundation for Science and Technology Development (NAFOSTED), grant no. 101.03-2015.11.

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Correspondence to Le Van Thanh.

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Van Thanh, L., Tu, N.N. Non-uniform Berry-Esseen Bounds for Coordinate Symmetric Random Vectors with Applications. Acta Math Vietnam 44, 893–904 (2019). https://doi.org/10.1007/s40306-018-00305-2

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Keywords

  • Non-uniform Berry-Esseen bound
  • Coordinate symmetric random vector
  • Rate of convergence
  • Cone measure
  • Volume measure

Mathematics Subject Classification (2010)

  • 60F05
  • 60D05
  • 52A20