A Combinatorial Central Limit Theorem

Hoeffding, Wassily

Ann. Math. Statist., Tome 22 (1951) no. 4, p. 558-566 / Harvested from Project Euclid

Résumé

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).

Publié le : 1951-12-14
Classification:

@article{1177729545,
     author = {Hoeffding, Wassily},
     title = {A Combinatorial Central Limit Theorem},
     journal = {Ann. Math. Statist.},
     volume = {22},
     number = {4},
     year = {1951},
     pages = { 558-566},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177729545}
}

Hoeffding, Wassily. A Combinatorial Central Limit Theorem. Ann. Math. Statist., Tome 22 (1951) no. 4, pp.  558-566. http://gdmltest.u-ga.fr/item/1177729545/