Uniform Local Probability Approximations: Improvements on Berry-Esseen
نویسندگان
چکیده
منابع مشابه
A Berry - Esseen bound for the uniform multinomial occupancy model ∗
The inductive size bias coupling technique and Stein’s method yield a Berry-Esseen theorem for the number of urns having occupancy d ≥ 2 when n balls are uniformly distributed over m urns. In particular, there exists a constant C depending only on d such that sup z∈R |P (Wn,m ≤ z)− P (Z ≤ z)| ≤ C σn,m 1 + ( n m )3 for all n ≥ d and m ≥ 2, where Wn,m and σ 2 n,m are the standardized count and va...
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Let λ be a partition of n chosen from the Plancherel measure of the symmetric group Sn, let χλ(12) be the irreducible character of the symmetric group parameterized by λ evaluated on the transposition (12), and let dim(λ) be the dimension of the irreducible representation parameterized by λ. Fulman recently obtained the convergence rate of O(n−s) for any 0 < s < 1 2 in the central limit theorem...
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An analogue of the Berry-Esseen inequality is proved for the speed of convergence of free additive convolutions of bounded probability measures. The obtained rate of convergence is of the order n, the same as in the classical case. An example with binomial measures shows that this estimate cannot be improved without imposing further restrictions on convolved measures. Courant Institute of Mathe...
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Berry Esseen type bounds to the normal, based on zeroand size-bias couplings, are derived using Stein’s method. The zero biasing bounds are illustrated with an application to combinatorial central limit theorems where the random permutation has either the uniform distribution or one which is constant over permutations with the same cycle type and having no fixed points. The size biasing bounds ...
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 1995
ISSN: 0091-1798
DOI: 10.1214/aop/1176988394