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A martingale approach to central limit theorems for exchangeable random variables

  • N. C. Weber (a1)

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.

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References

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Blum, J. R., Chernoff, H., Rosenblatt, M. and Teicher, H. (1958) Central limit theorems for interchangeable processes. Canad. J. Math. 10, 222229.
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Dvoretzky, A. (1972) Asymptotic normality for sums of dependent random variables. Proc. 6th Berkeley Symp. Math. Statist. Prob. 2, 513535.
Eagleson, G. K. (1975) Martingale convergence to mixtures of infinitely divisible laws. Ann. Prob. 3, 557562.
Eagleson, G. K. and Weber, N. C. (1978) Limit theorems for weakly exchangeable arrays. Math. Proc. Camb. Phil. Soc. 84, 123130.
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, 119137.

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A martingale approach to central limit theorems for exchangeable random variables

  • N. C. Weber (a1)

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