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April, 1973 A Central Limit Theorem for $m$-Dependent Random Variables with Unbounded $m$
Kenneth N. Berk
Ann. Probab. 1(2): 352-354 (April, 1973). DOI: 10.1214/aop/1176996992

Abstract

For each $k = 1, 2, \cdots$ let $n = n(k)$, let $m = m(k)$, and suppose $y_1^k, \cdots, y_n^k$ is an $m$-dependent sequence of random variables. We assume the random variables have $(2 + \delta)$th moments, that $m^{2 + 2/\delta}/n \rightarrow 0$, and other regularity conditions, and prove that $n^{-\frac{1}{2}}(y_1^k + \cdots + y_n^k)$ is asymptotically normal. An example showing sharpness is given.

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Kenneth N. Berk. "A Central Limit Theorem for $m$-Dependent Random Variables with Unbounded $m$." Ann. Probab. 1 (2) 352 - 354, April, 1973. https://doi.org/10.1214/aop/1176996992

Information

Published: April, 1973
First available in Project Euclid: 19 April 2007

zbMATH: 0263.60006
MathSciNet: MR350815
Digital Object Identifier: 10.1214/aop/1176996992

Keywords: $m$-dependent random variables , central limit theorem

Rights: Copyright © 1973 Institute of Mathematical Statistics

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Vol.1 • No. 2 • April, 1973
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