Abstract
The central limit theorem has been extended to the case of dependent random variables by several authors (Bruns, Markoff, S. Bernstein, P. Lévy, Loève). The conditions under which these theorems are stated either are very restrictive or involve conditional distributions, which makes them difficult to apply. In the present paper we prove central limit theorems for sequences of dependent random variables of a certain special type which occurs frequently in mathematical statistics. The hypotheses do not involve conditional distributions.
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References
T. W. Anderson and Herman Rubin, Estimation of the parameters of a single stochastic difference equation in a complete system, Cowles Commission Staff Papers, Statistics, January, 1947.
Serge Bernstein, Sur l’extension du théoréme limite du calcul des probabilités aux sommes de quantités dépendantes, Mathematische Annalen, vol. 97 (1927), pp. 1–59.
Harald Cramér, Mathematical Methods of Statistics, Princeton University Press, 1946.
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© 1994 Springer Science+Business Media New York
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Hoeffding, W., Robbins, H. (1994). The Central Limit Theorem for Dependent Random Variables. In: Fisher, N.I., Sen, P.K. (eds) The Collected Works of Wassily Hoeffding. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0865-5_9
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DOI: https://doi.org/10.1007/978-1-4612-0865-5_9
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6926-7
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