Title: The rate of convergence of some asymptotically chi-square distributed via Stein's method
Authors: Robert Gaunt - The University of Manchester (United Kingdom) [presenting]
Gesine Reinert - Oxford University (United Kingdom)
Abstract: Stein's method is a powerful technique for bounding the distance between two probability distributions with respect to a probability metric. We see how the classical Stein's method for normal approximation can be extended relatively easily via a general transfer principle to derive approximations for statistics that can be expressed as a function of a multivariate normal random variable. We also note a surprising result regarding the rate of convergence. This approach is used to derive a bound on the rate of convergence of Pearson's statistic to its limiting chi-square distribution. The bound has the correct dependence on the model parameters. We end by noting that our approach can also be applied to many other statistics, including Friedman's statistic and the family of power divergence statistics.