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We review the current state of statistical modeling of asymptotically independent data. Our discussion includes necessary and sufficient conditions for asymptotic independence, results on the asymptotic independence of statistics of interest, estimation and inference issues, joint tail modeling, and conditional approaches. For each of these topics we give an account of existing approaches and relevant methods for data analysis and applications.
Jan Steggemann, Konstantin Androsov, Anna Mascellani, Joanna Malgorzata Wanczyk, Paul Théodore Gabriel Pablo De Bryas Dexmiers d'Archiac