UCPH Statistics Seminar: Andreas Basse-O'Connor

Title: High-Dimensional Central Limit Theorems: Quantitative Bounds for Dependent Data

Speaker: Andreas Basse-O'Connor from Aarhus University

Abstract: The Central Limit Theorem (CLT) plays a crucial role as the theoretical cornerstone for a diverse range of statistical tests and estimators, empowering us to derive meaningful inferences about population parameters based on sample. In this talk, our objective is to provide quantitative bounds for CLTs, also known as Berry-Essen estimates.

With the increasing prevalence of high-dimensional datasets, there is a growing demand for understanding statistical estimation methods in high-dimensional settings. Therefore, our primary focus will be on quantifying the impact of dimensionality on the rate of convergence, commonly known as the curse of dimensionality.

More specifically, we will demonstrate that both short- and long-range dependent data exhibit a sub-polynomial dimensional dependence when evaluating the Gaussian approximation in the hyper-rectangle metric. To obtain these results, we will combine the power techniques of Stein's kernels and Malliavin Calculus. The talk is based on joint work with David Kramer-Bang.