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Asymptotic independence of median and MAD

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  • Falk, Michael

Abstract

The asymptotic joint normality of the sample median and the median absolute deviation from the median (MAD) as robust counterparts of sample mean and standard deviation is established. This characterizes their asymptotic independence, paralleling the asymptotic independence of mean and standard deviation. Analogous results are established for the median and the interquartile range.

Suggested Citation

  • Falk, Michael, 1997. "Asymptotic independence of median and MAD," Statistics & Probability Letters, Elsevier, vol. 34(4), pages 341-345, June.
    • Handle: RePEc:eee:stapro:v:34:y:1997:i:4:p:341-345
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    Citations

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    Cited by:

    1. Olive, David J., 2001. "High breakdown analogs of the trimmed mean," Statistics & Probability Letters, Elsevier, vol. 51(1), pages 87-92, January.
    2. Serfling, Robert & Mazumder, Satyaki, 2009. "Exponential probability inequality and convergence results for the median absolute deviation and its modifications," Statistics & Probability Letters, Elsevier, vol. 79(16), pages 1767-1773, August.
    3. Mazumder, Satyaki & Serfling, Robert, 2009. "Bahadur representations for the median absolute deviation and its modifications," Statistics & Probability Letters, Elsevier, vol. 79(16), pages 1774-1783, August.
    4. Nagatsuka, Hideki & Kawakami, Hiroshi & Kamakura, Toshinari & Yamamoto, Hisashi, 2013. "The exact finite-sample distribution of the median absolute deviation about the median of continuous random variables," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 999-1005.
    5. Zhiqiang Chen & Evarist Giné, 2004. "Another approach to asymptotics and bootstrap of randomly trimmed means," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(4), pages 771-790, December.
    6. Mahesh K.C & Arnab Kumar Laha, 2021. "A Robust Sharpe Ratio," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 444-465, November.

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