A1938
Title: Convex distance bounds for the stable central limit theorem via Steins method
Authors: Robert Gaunt - The University of Manchester (United Kingdom) [presenting]
Abstract: The stable central limit theorem is a generalisation of the classical central limit theorem that relaxes the finite variance assumption. Quantifying the quality of the distributional approximation of the stable central limit theorem is a fundamental problem in probability and mathematical statistics, which has seen numerous contributions over the years. In particular, there have been recent advances on this problem using the Stein method in which the stable central limit theorem is quantified with respect to Wasserstein type distances. Rates of convergence in the multivariate stable central limit theorem are derived in terms of the convex distance, which is a natural multivariate generalisation of the Kolmogorov distance, using Stein's method. Lower bounds are also presented to demonstrate optimality of the bounds in certain regimes. The bounds are derived by combining recent advances on the Stein method for alpha-stable distributions together with a powerful smoothing technique.
