Nicolai Palm (LMU München) :
Central limit theorems under non-stationarity via relative weak convergence
Zeit und Ort
Freitag, 15.11.24, 13:00-14:00, Raum 232, Ernst-Zermelo-Str. 1
Zusammenfassung
Traditional central limit theorems (CLTs) have limited applicability to non-stationary sequences, restricting their use in real-world, dynamic data contexts. We introduce relative weak convergence, a generalisation of classical weak convergence that provides a natural framework for CLTs in non-stationary settings. Within this framework we can prove multivariate, uniform, and sequential relative CLTs for dynamic sequences under general assumptions. These results bridge a critical gap in asymptotic statistics, enabling researchers to rigorously study the asymptotic behaviour of dynamic sequences that do not satisfy traditional assumptions of stationarity.