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Central limit theorems for the Wasserstein distance between the empirical and the true distributions. (English) Zbl 0958.60012
Ann. Probab. 27, No. 2, 1009-1071 (1999); correction ibid. 31, No. 2, 1142-1143 (2003).
For a sequence of i.i.d. random variables, it is well-known that the Wassertein distance between their empirical distribution and the true distribution tends to zero. The rate of this convergence is studied. As a by-product, some limit theorems for the Ornstein-Uhlenbeck processes are also derived.
Reviewer: D.Tu (Kingston)

MSC:
60F05 Central limit and other weak theorems
60F17 Functional limit theorems; invariance principles
62E20 Asymptotic distribution theory in statistics
62G30 Order statistics; empirical distribution functions
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