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A Combinatorial Central Limit Theorem
Open accessAbstract
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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Metadata
- Authors
- Hoeffding, W.
- Venue
- The Annals of Mathematical Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 1951-12
- Volume
- 22
- Issue
- 4
- Pages
- 558-566
- ISSN
- 0003-4851 (ISSN-L)
- OpenAlex
- W4255170875
- Cited by
- 197
- References
- 0
- FWCI
- 1.74
- Type
- journal article
- Language
- en
- Open access
- bronze
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