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Estimating an endpoint with high-order moments

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  • Stéphane Girard
  • Armelle Guillou
  • Gilles Stupfler

Abstract

We present a new method for estimating the endpoint of a unidimensional sample when the distribution function decreases at a polynomial rate to zero in the neighborhood of the endpoint. The estimator is based on the use of high-order moments of the variable of interest. It is assumed that the order of the moments goes to infinity, and we give conditions on its rate of divergence to get the asymptotic normality of the estimator. The good performance of the estimator is illustrated on some finite sample situations. Copyright Sociedad de Estadística e Investigación Operativa 2012

Suggested Citation

  • Stéphane Girard & Armelle Guillou & Gilles Stupfler, 2012. "Estimating an endpoint with high-order moments," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(4), pages 697-729, December.
    • Handle: RePEc:spr:testjl:v:21:y:2012:i:4:p:697-729
    DOI: 10.1007/s11749-011-0277-8
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    References listed on IDEAS

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    1. Goldenshluger, A. & Tsybakov, A., 2004. "Estimating the endpoint of a distribution in the presence of additive observation errors," Statistics & Probability Letters, Elsevier, vol. 68(1), pages 39-49, June.
    2. Einmahl, J. H.J. & Dekkers, A. L.M. & de Haan, L., 1989. "A moment estimator for the index of an extreme-value distribution," Other publications TiSEM 81970cb3-5b7a-4cad-9bf6-2, Tilburg University, School of Economics and Management.
    3. 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.
    4. Neves, Cláudia & Pereira, António, 2010. "Detecting finiteness in the right endpoint of light-tailed distributions," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 437-444, March.
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    Cited by:

    1. 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.
    2. 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.
    3. Matheus Henrique Junqueira Saldanha & Adriano Kamimura Suzuki, 2023. "On dealing with the unknown population minimum in parametric inference," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 107(3), pages 509-535, September.

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