Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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A Sufficient Condition on Optimal Berry-Esseen Bounds of Functionals of Gaussian Fields

  • Kim, Yoon Tae (Department of Finance and Information Statistics, Hallym University)
  • Received : 2012.07.12
  • Accepted : 2012.11.21
  • Published : 2013.01.31
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Abstract

We find a sufficient condition for optimal Berry-Esseen bounds in the normal approximation of functionals of Gaussian fields studied by Nourdin and Peccati (2009b).

Keywords

Acknowledgement

Supported by : National Research Foundation of Korea(NRF)

References

  1. Billingsley, P. (1968). Converges of Probability Measures, John Wiley & Sons, Inc.
  2. Nourdin, I. and Peccati, G. (2009a). Stein's method onWiener Chaos, Probability Theory and Related Fields, 145, 75-118. https://doi.org/10.1007/s00440-008-0162-x
  3. Nourdin, I. and Peccati, G. (2009b). Stein's method and exact Berry-Esseen asymptotics for functionals of Gaussian fields, Annals of Probability, 37, 2231-2261. https://doi.org/10.1214/09-AOP461
  4. Nualart, D. (2006). Malliavin Calculus and Related Topics, 2nd Ed., Springer.