B0836
Title: Bounds for distributional approximation in the multivariate delta method by Steins method
Authors: Robert Gaunt - The University of Manchester (United Kingdom) [presenting]
Abstract: Bounds are presented that quantify the distributional approximation in the delta method for vector statistics (the sample mean of n independent random vectors) for normal and non-normal limits, measured using smooth test functions. For normal limits, the bounds are of the optimal order $1/n^(1/2)$ rate, but for a wide class of non-normal limits, which includes quadratic forms amongst others, the bounds have a faster order $1/n$ convergence rate. Some illustrative examples are presented, including a statistic for Bernoulli variance, statistics based on sample moments, and some classic chi-square test statistics. It is briefly seen how the general results are derived through generalisations of recent results on Stein's method for functions of multivariate normal random vectors.
