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THE ERDÖS-TURÁN LAW FOR MIXTURES OF DIRICHLET PROCESSES (II)

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Abstract Let a random distribution P on the real line R have the mixture of Dirichlet processes. Let S^<(n)>=(S_1, …, S_n) be the random partition of the positive integer n based on a sample of size n from P. For the order O_n(S^<(n)>) of S^<(n)>, Yamato (2013) gives the asymptotic distribution of the statistic log O_n(S^<(n)>)/log^2 n and the rate O(1/log^<1/3>n) of its convergence. In this pager we give the Edgeworth expansions for the statistic with the rates O(1/log^<2/5>n) and O(1/log^<3/7>n). In addition, we correct the errors of the proofs of the lemmas 2.5 and 2.6 of Yamato (2013).

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Created Date 2017.03.15
Modified Date 2017.04.07