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Acta Mathematica Vietnamica

, Volume 44, Issue 4, pp 893–904 | Cite as

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

  • Le Van ThanhEmail author
  • Nguyen Ngoc Tu
Article
  • 59 Downloads

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.

Keywords

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

Mathematics Subject Classification (2010)

60F05 60D05 52A20 

Notes

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 Information

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

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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Department of MathematicsVinh UniversityVinhVietnam
  2. 2.Department of Applied SciencesHCMC University of Technology and EducationHo Chi Minh CityVietnam
  3. 3.Department of Mathematics and Computer ScienceHo Chi Minh City National UniversityHo Chi Minh CityVietnam

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