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A smoothing stochastic algorithm for quantile estimation

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  • Amiri, Aboubacar
  • Thiam, Baba

Abstract

In this paper, we provide the almost-sure convergence and the asymptotic normality of a smooth version of the Robbins–Monro algorithm for the quantile estimation. A Monte Carlo simulation study shows that our proposed method works well within the framework of a data stream.

Suggested Citation

  • Amiri, Aboubacar & Thiam, Baba, 2014. "A smoothing stochastic algorithm for quantile estimation," Statistics & Probability Letters, Elsevier, vol. 93(C), pages 116-125.
    • Handle: RePEc:eee:stapro:v:93:y:2014:i:c:p:116-125
    DOI: 10.1016/j.spl.2014.06.016
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    References listed on IDEAS

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    1. Cai, Zongwu & Wang, Xian, 2008. "Nonparametric estimation of conditional VaR and expected shortfall," Journal of Econometrics, Elsevier, vol. 147(1), pages 120-130, November.
    2. Gourieroux, C. & Laurent, J. P. & Scaillet, O., 2000. "Sensitivity analysis of Values at Risk," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 225-245, November.
    3. Robert F. Engle & Simone Manganelli, 2004. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 367-381, October.
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    Cited by:

    1. Camirand Lemyre, Felix & Decrouez, Geoffrey, 2021. "Nonparametric recursive estimation of the copula," Statistics & Probability Letters, Elsevier, vol. 168(C).

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