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Frontier estimation via kernel regression on high power-transformed data

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  • Girard, Stéphane
  • Jacob, Pierre
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    Abstract

    We present a new method for estimating the frontier of a multidimensional sample. The estimator is based on a kernel regression on the power-transformed data. We assume that the exponent of the transformation goes to infinity while the bandwidth of the kernel goes to zero. We give conditions on these two parameters to obtain complete convergence and asymptotic normality. The good performance of the estimator is illustrated on some finite sample situations.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 99 (2008)
    Issue (Month): 3 (March)
    Pages: 403-420

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    Handle: RePEc:eee:jmvana:v:99:y:2008:i:3:p:403-420

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    Keywords: Kernel estimator Power-transform Frontier estimation;

    References

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    1. Hall, Peter & Park, Byeong U., 2004. "Bandwidth choice for local polynomial estimation of smooth boundaries," Journal of Multivariate Analysis, Elsevier, vol. 91(2), pages 240-261, November.
    2. Stéphane Girard, 2003. "Extreme Values and Haar Series Estimates of Point Process Boundaries," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 30(2), pages 369-384.
    3. repec:wop:humbsf:1998-9 is not listed on IDEAS
    4. Tsybakov, A.B. & Korostelev, A.P. & Simar, L., 1992. "Efficient Estimation of Monotone Boundaries," Papers 9209, Catholique de Louvain - Institut de statistique.
    5. Cazals, Catherine & Florens, Jean-Pierre & Simar, Leopold, 2002. "Nonparametric frontier estimation: a robust approach," Journal of Econometrics, Elsevier, vol. 106(1), pages 1-25, January.
    6. Jacob, P. & Suquet, Ch., 1996. "Regression and edge estimation," Statistics & Probability Letters, Elsevier, vol. 27(1), pages 11-15, March.
    7. Hall, Peter & Nussbaum, Michael & Stern, Steven E., 1997. "On the Estimation of a Support Curve of Indeterminate Sharpness," Journal of Multivariate Analysis, Elsevier, vol. 62(2), pages 204-232, August.
    8. Hardle, W. & Park, B. U. & Tsybakov, A. B., 1995. "Estimation of Non-sharp Support Boundaries," Journal of Multivariate Analysis, Elsevier, vol. 55(2), pages 205-218, November.
    9. Aragon, Y. & Daouia, A. & Thomas-Agnan, C., 2005. "Nonparametric Frontier Estimation: A Conditional Quantile-Based Approach," Econometric Theory, Cambridge University Press, vol. 21(02), pages 358-389, April.
    10. Hall, Peter & Park, Byeong U. & Stern, Steven E., 1998. "On Polynomial Estimators of Frontiers and Boundaries," Journal of Multivariate Analysis, Elsevier, vol. 66(1), pages 71-98, July.
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    Cited by:
    1. 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.
    2. Abdelaati Daouia & Laurent Gardes & Stéphane Girard & Alexandre Lekina, 2011. "Kernel estimators of extreme level curves," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 20(2), pages 311-333, August.
    3. Girard, Stéphane & Guillou, Armelle & Stupfler, Gilles, 2013. "Frontier estimation with kernel regression on high order moments," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 172-189.
    4. Girard, Séphane & Jacob, Pierre, 2009. "Frontier estimation with local polynomials and high power-transformed data," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1691-1705, September.

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