Upper bounds for minimal distances in the central limit theorem
نویسندگان
چکیده
منابع مشابه
Rates of convergence for minimal distances in the central limit theorem under projective criteria
In this paper, we give estimates of ideal or minimal distances between the distribution of the normalized partial sum and the limiting Gaussian distribution for stationary martingale difference sequences or stationary sequences satisfying projective criteria. Applications to functions of linear processes and to functions of expanding maps of the interval are given.
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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: Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
سال: 2009
ISSN: 0246-0203
DOI: 10.1214/08-aihp187