Central limit theorems under non-stationarity via relative weak convergence |
Nicolai Palm (LMU München) |
Friday, 2024-11-15 13:00 |
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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. |