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December, 1951 A Combinatorial Central Limit Theorem
Wassily Hoeffding
Ann. Math. Statist. 22(4): 558-566 (December, 1951). DOI: 10.1214/aoms/1177729545


Let $(Y_{n1}, \cdots, Y_{nn})$ be a random vector which takes on the $n!$ permutations of $(1, \cdots, n)$ with equal probabilities. Let $c_n(i, j), i,j = 1, \cdots, n,$ be $n^2$ real numbers. Sufficient conditions for the asymptotic normality of $S_n = \sum^n_{i=1} c_n(i, Y_{ni})$ are given (Theorem 3). For the special case $c_n(i,j) = a_n(i)b_n(j)$ 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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Wassily Hoeffding. "A Combinatorial Central Limit Theorem." Ann. Math. Statist. 22 (4) 558 - 566, December, 1951.


Published: December, 1951
First available in Project Euclid: 28 April 2007

zbMATH: 0044.13702
MathSciNet: MR44058
Digital Object Identifier: 10.1214/aoms/1177729545

Rights: Copyright © 1951 Institute of Mathematical Statistics

Vol.22 • No. 4 • December, 1951
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