Abstract
In this paper, we introduce a scheme of summation of independent random variables with random replacements. We consider a series of double arrays of identically distributed random variables that are row-wise independent, but such that neighboring rows contain a random common part of the repeating terms. By this-scheme we bscribe a model of strongly dependent noise. To investigate the sample mean of this noise, we consider the sum of random variables over the whole double array and its conditional variance with respect to replacements. For columns of the arrays we prove a covariance inequality. As a corollary of it, we demonstrate the law of large numbers for conditional variances. Bibliography: 4 titles.
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References
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Additional information
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 216, 1994, pp. 124–143.
Translated by A. Sudakov.
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Rusakov, O.V. Asymptotical behavior of the variance of sums of random variables with random replacements. J Math Sci 88, 86–98 (1998). https://doi.org/10.1007/BF02363267
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DOI: https://doi.org/10.1007/BF02363267