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A sharp estimate of the binomial mean absolute deviation with applications

Author

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  • Berend, Daniel
  • Kontorovich, Aryeh

Abstract

We give simple, sharp non-asymptotic bounds on the mean absolute deviation (MAD) of a Bin(n,p) random variable. Although MAD is known to behave asymptotically as the standard deviation, the convergence is not uniform over the range of p and fails at the endpoints. Our estimates hold for all p∈[0,1] and illustrate a simple transition from the “linear” regime near the endpoints to the “square root” regime elsewhere. As an application, we provide asymptotically optimal tail estimates of the total variation distance between the empirical and the true distributions over countable sets.

Suggested Citation

  • Berend, Daniel & Kontorovich, Aryeh, 2013. "A sharp estimate of the binomial mean absolute deviation with applications," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1254-1259.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:4:p:1254-1259
    DOI: 10.1016/j.spl.2013.01.023
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    Cited by:

    1. Negin Gorlezaei & Patrick Jaillet & Zijie Zhou, 2022. "Online Resource Allocation with Samples," Papers 2210.04774, arXiv.org.
    2. Pelekis, Christos & Ramon, Jan, 2016. "A lower bound on the probability that a binomial random variable is exceeding its mean," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 305-309.

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