Rates of convergence for multivariate normal approximations by Stein's method

Robert Gaunt (University of Manchester)

Frank Adams 2,

(This seminar was originally scheduled for 1 March 2017.)

Stein's method is a powerful technique for obtaining distributional approximations in probability theory.  We begin by reviewing Stein’s method for normal approximation.  We then consider how this approach can be adapted to limits other than the normal.  In particular, we see how Stein’s method for normal approximation can be extended relatively easily to the approximation of statistics that are asymptotically distributed as functions of multivariate normal random variables.  We obtain some general bounds and a surprising result regarding the rate of convergence.  We end with an application to the rate of convergence of Pearson's chi-square statistic. 

Part of this talk is based on joint work with Alastair Pickett and Gesine Reinert.

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