Abstract
A collection of random variables is defined to be interchangeable if every finite subcollection has a joint distribution which is a symmetric function of its arguments. Double sequences of random variables $X_{nk}, k = 1, 2, \cdots, k_n (\rightarrow \infty), n = 1, 2, \cdots$, interchangeable (as opposed to independent) within rows, are considered. For each $n, X_{n1}, \cdots, X_{n,k_n}$ may (a) have a non-random sum, or (b) be embeddable in an infinite sequence of interchangeable random variables, or (c) neither. In case (a), a theorem is obtained providing conditions under which the partial sums have a limiting normal distribution. Applications to such well-known examples as ranks and percentiles are exhibited. Case (b) is treated elsewhere while case (c) remains open.
Citation
H. Chernoff. H. Teicher. "A Central Limit Theorem for Sums of Interchangeable Random Variables." Ann. Math. Statist. 29 (1) 118 - 130, March, 1958. https://doi.org/10.1214/aoms/1177706709
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