A1278
Title: Weak dependence and optimal quantitative self-normalized central limit theorems
Authors: Moritz Jirak - University of Vienna (Austria) [presenting]
Abstract: Consider a stationary, weakly dependent sequence of random variables. Given that a CLT holds, how should the long-run variance be estimated? This problem has been studied for decades, and prominent proposed solutions have been given. Using the proximity of the corresponding normal distribution as a quality measure, optimal solutions and why previous proposals are not optimal in this context discussed. The setup contains many prominent dynamical systems and time series models, including random walks on the general linear group, products of positive random matrices, functionals of Garch models of any order, functionals of dynamical systems arising from SDEs, iterated random functions and many more.
