Explicit rates of convergence in the multivariate CLT for nonlinear statistics

  • N. T. DungEmail author


We investigate the multivariate central limit theorem for nonlinear statistics by means of Stein’s method and Slepian’s smart path interpolation method. Based on certain difference operators in the theory of concentration inequalities, we obtain two explicit bounds for the rate of convergence. Applications to Rademacher functionals, the runs and quadratic forms are provided as well.

Key words and phrases

multivariate normal approximation Stein’s method Slepian’s interpolation method difference operator 

Mathematics Subject Classification

60F05 62E17 


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The author thanks the anonymous referee for valuable comments for improving the paper.


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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.Division of Computational Mathematics and Engineering, Institute for Computational ScienceTon Duc Thang UniversityHo Chi Minh CityVietnam
  2. 2.Faculty of Mathematics and StatisticsTon Duc Thang UniversityHo Chi Minh CityVietnam

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