Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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KOLMOGOROV DISTANCE FOR MULTIVARIATE NORMAL APPROXIMATION

  • Kim, Yoon Tae (Department of Finance and Information Statistics Hallym University) ;
  • Park, Hyun Suk (Department of Finance and Information Statistics Hallym University)
  • Received : 2014.10.14
  • Accepted : 2015.01.19
  • Published : 2015.03.30
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Abstract

This paper concerns the rate of convergence in the multidimensional normal approximation of functional of Gaussian fields. The aim of the present work is to derive explicit upper bounds of the Kolmogorov distance for the rate of convergence instead of Wasserstein distance studied by Nourdin et al. [Ann. Inst. H. Poincar$\acute{e}$(B) Probab.Statist. 46(1) (2010) 45-98].

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References

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Cited by

  1. Multivariate second order Poincaré inequalities for Poisson functionals vol.24, pp.None, 2015, https://doi.org/10.1214/19-ejp386
  2. High-dimensional central limit theorems by Stein’s method vol.31, pp.4, 2021, https://doi.org/10.1214/20-aap1629