On the characteristic function of a sum of M -dependent random variables

Wansoo T. Rhee

International Journal of Mathematics and Mathematical Sciences, 1986, vol. 9, 1-8

Abstract:

Let S = f 1 + f 2 + … + f n be a sum of 1 -dependent random variables of zero mean. Let σ 2 = E S 2 , L = σ − 3 ∑ 1 ≦ i ≦ n E | f i | 3 . There is a universal constant a such that for a | t | L < 1 , we have | E exp ( i t S σ − 1 ) | ≦ ( 1 + a | t | ) sup { ( a | t | L ) − 1 / 4 ln L , exp ( − t 2 / 80 ) } . This bound is a very useful tool in proving Berry-Esseen theorems.

Date: 1986
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:781385

DOI: 10.1155/S0161171286000492

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