Kolmogorov distance for multivariate normal approximation
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This paper concerns the rate of convergence in the mul- tidimensional 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 Wasser- stein distance studied by Nourdin et al. [Ann. Inst. H. Poincar ́e(B) Probab.Statist. 46(1) (2010) 45-98].
Abstract
This paper concerns the rate of convergence in the mul- tidimensional 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 Wasser- stein distance studied by Nourdin et al. [Ann. Inst. H. Poincar ́e(B) Probab.Statist. 46(1) (2010) 45-98].
참고문헌 (10)
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- Nourdin, I., "Multivariate normal approximation using Stein's method and Malliavin calculus", Ann. Inst. H. Poincarlle(B)Probab.Statist., 46(1), pp.45~98 (2010)
- D. Nualart, "Malliavin calculus and related topics" (2006), Springer