期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2016
卷号：XIII
期号：2
页码：1165-1187
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：A consequence of de Finetti's representation theorem is that for everyin nite sequence of exchangeable 0-1 random variables (Xk)k1, there exists aprobability measure on the Borel sets of [0; 1] such that Xn = n1Pni=1 Xiconverges weakly to . For a wide class of probability measures having smoothdensity on (0; 1), we give bounds of order 1=n with explicit constants for theWasserstein distance between the law of Xn and . This extends a recent result byGoldstein and Reinert (2013) regarding the distance between the scaled numberof white balls drawn in a Polya-Eggenberger urn and its limiting distribution. Weprove also that, in the most general cases, the distance between the law of Xn and is bounded below by 1=n and above by 1=pn (up to some multiplicative constants).For every 2 [1=2; 1], we give an example of an exchangeable sequence such thatthis distance is of order 1=n.
