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Estimating an endpoint with high order moments in the Weibull domain of attraction

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  • Girard, Stéphane
  • Guillou, Armelle
  • Stupfler, Gilles

Abstract

We present a method for estimating the endpoint of a unidimensional sample when the distribution function belongs to the Weibull-max domain of attraction. The approach relies on transforming the variable of interest and then using high order moments of the positive variable obtained this way. It is assumed that the order of the moments goes to infinity. We give conditions on the rate of divergence to get the weak and strong consistency as well as the asymptotic normality of the estimator. The good performance of the estimator is illustrated on some finite sample situations.

Suggested Citation

  • Girard, Stéphane & Guillou, Armelle & Stupfler, Gilles, 2012. "Estimating an endpoint with high order moments in the Weibull domain of attraction," Statistics & Probability Letters, Elsevier, vol. 82(12), pages 2136-2144.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:12:p:2136-2144
    DOI: 10.1016/j.spl.2012.07.005
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    References listed on IDEAS

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    1. Peter Hall & Julian Z. Wang, 2005. "Bayesian likelihood methods for estimating the end point of a distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 717-729, November.
    2. Girard, Stéphane & Jacob, Pierre, 2008. "Frontier estimation via kernel regression on high power-transformed data," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 403-420, March.
    3. Deyuan Li & Liang Peng & Yongcheng Qi, 2011. "Empirical likelihood confidence intervals for the endpoint of a distribution function," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 353-366, August.
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    Cited by:

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    2. Daouia, Abdelaati & Girard, Stéphane & Guillou, Armelle, 2014. "A Γ-moment approach to monotonic boundary estimation," Journal of Econometrics, Elsevier, vol. 178(2), pages 727-740.
    3. Hong-Jiang Wu & Ying-Ying Zhang & Han-Yu Li, 2023. "Expectation identities from integration by parts for univariate continuous random variables with applications to high-order moments," Statistical Papers, Springer, vol. 64(2), pages 477-496, April.

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