Title: Chi-square approximation by Stein's method with application to Pearson's statistic
Authors: Robert Gaunt - The University of Manchester (United Kingdom) [presenting]
Abstract: The Stein method for chi-square approximations is reviewed and some recent developments are discussed. We apply this theory to bind the distributional distance between Pearsons statistic and its limiting chi-square distribution, measured using smooth test functions. In combination with the use of symmetry arguments, Steins method yields explicit bounds on this distributional distance of order $1/n$. This bound also has the correct dependence on the cell classification probabilities, and we obtain a Kolmogorov distance bound which shares this property.