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Refinements of first order asymptotic results are reviewed, with a number of Ph.D. projects supervised by van Zwet serving as stepping stones. Berry-Esseen bounds and Edgeworth expansions are discussed for R-, L- and U-statistics. After these special classes, the question about a general second order theory for asymptotically normal statistics is addressed. As a final topic, empirical Edgeworth expansions are considere

From A to Z: asymptotic expansions by van Zwet