Berry–Esseen bounds in the entropic central limit theorem
نویسندگان
چکیده
منابع مشابه
Berry–Esseen bounds in the entropic central limit theorem
Berry–Esseen-type bounds for total variation and relative entropy distances to the normal law are established for the sums of non-i.i.d. random variables.
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Let E = ((eij))n×n be a fixed array of real numbers such that eij = eji, eii = 0 for 1 ≤ i, j ≤ n. Let the permutation group be denoted by Sn and the collection of involutions with no fixed points by Πn, that is, Πn = {π ∈ Sn : π = id, π(i) 6= i∀i} with id denoting the identity permutation. For π uniformly chosen from Πn, let YE = ∑n i=1 eiπ(i) and W = (YE − μE)/σE where μE = E(YE) and σ 2 E = ...
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Let E = ((eij))n×n be a fixed array of real numbers such that eij = eji, eii = 0 for 1 ≤ i, j ≤ n. Let the symmetric group be denoted by Sn and the collection of involutions with no fixed points by Πn, that is, Πn = {π ∈ Sn : π 2 = id, π(i) 6= i∀i}. For π uniformly chosen from Πn, let YE = Pn i=1 eiπ(i) and W = (YE − μE)/σE where μE = E(YE) and σ 2 E = Var(YE). Denoting by FW and Φ the distribu...
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ژورنال
عنوان ژورنال: Probability Theory and Related Fields
سال: 2013
ISSN: 0178-8051,1432-2064
DOI: 10.1007/s00440-013-0510-3