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Probabilities of the deviation of the sample mean from its median

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Abstract

One investigates the asymptotic behavior of\(P\left( {\bar X_n - med \bar X_n \geqslant \varepsilon } \right)\) as n→∞, where\(\bar X_n \) is the sample mean constructed from the independent, identically distributed random variables X1...,Xn, ɛ>0. One considers the powerlike and the exponential rates of decrease of this probability.

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Authors
  1. A. I. Martikainen
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 130, pp. 130–136, 1983.

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Martikainen, A.I. Probabilities of the deviation of the sample mean from its median. J Math Sci 27, 3258–3263 (1984). https://doi.org/10.1007/BF01850674

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  • DOI: https://doi.org/10.1007/BF01850674

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