On the error bound in a combinatorial central limit theorem
نویسنده
چکیده
Let X = {Xij : 1 ≤ i, j ≤ n} be an n× n array of independent random variables where n ≥ 2. Let π be a uniform random permutation of {1,2, . . . , n}, independent of X, and let W =∑ni=1 Xiπ(i). Suppose X is standardized so that EW = 0,Var(W)= 1. We prove that the Kolmogorov distance between the distribution of W and the standard normal distribution is bounded by 451 ∑n i,j=1 E|Xij |3/n. Our approach is by Stein’s method of exchangeable pairs and the use of a concentration inequality.
منابع مشابه
عدد تناوبی گرافها
In 2015, Alishahi and Hajiabolhassan introduced the altermatic number of graphs as a lower bound for the chromatic number of them. Their proof is based on the Tucker lemma, a combinatorial counterpart of the Borsuk-Ulam theorem, which is a well-known result in topological combinatorics. In this paper, we present a combinatorial proof for the Alishahi-Hajiabolhassan theorem.
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