Stein's method for functions of multivariate normal random variables

Journal article

It is a well-known fact that if the random vector W converges in distribution to a multivariate normal random variable Σ1/2Z, the g(W) converges in distribution to g(Σ1/2Z) if g is continuous. In this paper, we develop a general method for deriving bounds on the distributional distance between g(W) and g(Σ1/2Z). To illustrate this method, we obtain several bounds for the case that the j-component of W is given by Wj = n-1/2 Σni=1 Xij, where the Xij are independent. In particular...

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Authors: Gaunt, R

• Journal: arXiv
• Publication date: 2015-01-01
• Acceptance date: 2015-07-30
• Keywords: rate of convergence; functions of multivariate normal random variables; Stein's method; multivariate normal approximation
• Subjects: Primary 60F05