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On probabilistic properties of conditional medians and quantiles

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  • Ghosh, Yashowanto N.
  • Mukherjee, Bhramar

Abstract

Conditional medians and quantiles are frequently used in analyzing time series data with heavy tails for their robustness properties. Most of the available literature focusses on statistical estimation of conditional quantiles and large sample behavior of the proposed estimators, whereas probabilistic properties of the true conditional medians themselves have not been fully explored (Tomkins [1975. On conditional medians. Ann. Probab. 3, 375-379; 1978. Convergence properties of conditional medians. Canad. J. Statist. 6, 169-177]). It is well-known that not all properties of conditional expectations have analogues for conditional medians. In this short note, we study to what extent analogues of certain properties of conditional expectations hold for conditional medians and generalize some of these properties to any general conditional quantile.

Suggested Citation

  • Ghosh, Yashowanto N. & Mukherjee, Bhramar, 2006. "On probabilistic properties of conditional medians and quantiles," Statistics & Probability Letters, Elsevier, vol. 76(16), pages 1775-1780, October.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:16:p:1775-1780
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    References listed on IDEAS

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    1. Peter Hall & Liang Peng & Qiwei Yao, 2002. "Prediction and nonparametric estimation for time series with heavy tails," Journal of Time Series Analysis, Wiley Blackwell, vol. 23(3), pages 313-331, May.
    2. Hall, Peter & Peng, Liang & Yao, Qiwei, 2002. "Prediction and nonparametric estimation for time series with heavy tails," LSE Research Online Documents on Economics 6086, London School of Economics and Political Science, LSE Library.
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    Cited by:

    1. Augustynowicz, Aneta, 2020. "Asymptotic behavior of proportions of observations falling to random regions determined by central order statistics," Statistics & Probability Letters, Elsevier, vol. 162(C).
    2. Danúbia R. Cunha & Roberto Vila & Helton Saulo & Rodrigo N. Fernandez, 2020. "A General Family of Autoregressive Conditional Duration Models Applied to High-Frequency Financial Data," JRFM, MDPI, vol. 13(3), pages 1-20, March.
    3. Dembińska, Anna, 2014. "Asymptotic behavior of central order statistics from stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 348-372.
    4. Anna Dembińska, 2017. "An ergodic theorem for proportions of observations that fall into random sets determined by sample quantiles," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(3), pages 319-332, April.

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