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A martingale approach to central limit theorems for exchangeable random variables

Published online by Cambridge University Press:  14 July 2016

N. C. Weber
N. C. Weber*
Affiliation:
University of Cambridge
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Abstract

In this paper it will be shown that by an appropriate choice of σ-fields, martingale methods can be used to obtain simple proofs of many of the central limit theorems known for triangular arrays of exchangeable random variables.

Keywords

EXCHANGEABLE RANDOM VARIABLESMARTINGALESCENTRAL LIMIT THEOREMINVARIANCE PRINCIPLEREVERSED MARTINGALESTRIANGULAR ARRAYS
Type
Research Papers
Information
Journal of Applied Probability , Volume 17 , Issue 3 , September 1980 , pp. 662 - 673
Copyright
Copyright © Applied Probability Trust 1980 

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References

Blum, J. R., Chernoff, H., Rosenblatt, M. and Teicher, H. (1958) Central limit theorems for interchangeable processes. Canad. J. Math. 10, 222–229.Google Scholar
Chernoff, H. and Teicher, H. (1958) A central limit theorem for sums of interchangeable random variables. Ann. Math. Statist. 29, 118–130.Google Scholar
De Finetti, B. (1930) Funzione caratteristica di un fenomeno aleatorio. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. 4, 86–133.Google Scholar
Doob, J. L. (1953) Stochastic Processes. Wiley, New York.Google Scholar
Dvoretzky, A. (1972) Asymptotic normality for sums of dependent random variables. Proc. 6th Berkeley Symp. Math. Statist. Prob. 2, 513–535.Google Scholar
Eagleson, G. K. (1975) Martingale convergence to mixtures of infinitely divisible laws. Ann. Prob. 3, 557–562.Google Scholar
Eagleson, G. K. and Weber, N. C. (1978) Limit theorems for weakly exchangeable arrays. Math. Proc. Camb. Phil. Soc. 84, 123–130.Google Scholar
Scott, D. J. (1973) Central limit theorems for marring's and for processes with stationary increments using a Skorokhod representation approach. Adv. Appl. Prob. 5, 119–137.CrossRefGoogle Scholar