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Limit theorems for boundary function estimators

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  • Hwang, J. H.
  • Park, B. U.
  • Ryu, W.

Abstract

Park et al. (Econometric Theory 16 (2000) 855) and Gijbels et al. (J. Amer. Statist. Assoc. 94 (1999) 220) derived the limit distributions of the two most popular nonparametric estimators, FDH and DEA, of a boundary in a setting where the density or intensity of the data has a sharp or fault-type boundary. In this paper, we extend their results to the general case where the density or intensity may decrease to zero or infinity at a speed of power [alpha]-1 ([alpha]>0) of the distance from the boundary.

Suggested Citation

  • Hwang, J. H. & Park, B. U. & Ryu, W., 2002. "Limit theorems for boundary function estimators," Statistics & Probability Letters, Elsevier, vol. 59(4), pages 353-360, October.
    • Handle: RePEc:eee:stapro:v:59:y:2002:i:4:p:353-360
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    References listed on IDEAS

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    1. Park, B.U. & Simar, L. & Weiner, Ch., 2000. "The Fdh Estimator For Productivity Efficiency Scores," Econometric Theory, Cambridge University Press, vol. 16(6), pages 855-877, December.
    2. 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.
    3. 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.
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    Cited by:

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    2. Abdelaati Daouia & Léopold Simar & Paul W. Wilson, 2017. "Measuring firm performance using nonparametric quantile-type distances," Econometric Reviews, Taylor & Francis Journals, vol. 36(1-3), pages 156-181, March.
    3. Daouia, Abdelaati & Florens, Jean-Pierre & Simar, Léopold, 2009. "Frontier Estimation and Extreme Values Theory," IDEI Working Papers 611, Institut d'Économie Industrielle (IDEI), Toulouse.
    4. Abdelaati Daouia & Hohsuk Noh & Byeong U. Park, 2016. "Data envelope fitting with constrained polynomial splines," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(1), pages 3-30, January.
    5. Jeong, Seok-Oh & Simar, Léopold, 2006. "Linearly interpolated FDH efficiency score for nonconvex frontiers," Journal of Multivariate Analysis, Elsevier, vol. 97(10), pages 2141-2161, November.

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