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Journal Article

A Combinatorial Central Limit Theorem

Wassily Hoeffding
The Annals of Mathematical Statistics
Vol. 22, No. 4 (Dec., 1951), pp. 558-566
Stable URL: http://www.jstor.org/stable/2236924
Page Count: 9

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Topics: Central limit theorem, Integers, Real numbers, Random variables
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
A Combinatorial Central Limit Theorem
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Abstract

Let (Yn1, ⋯, Ynn) be a random vector which takes on the n! permutations of (1, ⋯, n) with equal probabilities. Let cn(i, j), i,j = 1, ⋯, n, be n2 real numbers. Sufficient conditions for the asymptotic normality of Sn = ∑n i=1 cn(i, Yni) are given (Theorem 3). For the special case cn(i,j) = an(i)bn(j) a stronger version of a theorem of Wald, Wolfowitz and Noether is obtained (Theorem 4). A condition of Noether is simplified (Theorem 1).

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