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Estimating the endpoint of a distribution in the presence of additive observation errors

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  • Goldenshluger, A.
  • Tsybakov, A.

Abstract

We consider the problem of estimating the endpoint of a probability distribution in the presence of observation errors, when the available sample is drawn from the convolution with some error density. We study the cases of Gaussian errors and errors with bounded support, and propose estimators that are optimal in a minimax sense.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:68:y:2004:i:1:p:39-49
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    References listed on IDEAS

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    1. Hall P. & Simar L., 2002. "Estimating a Changepoint, Boundary, or Frontier in the Presence of Observation Error," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 523-534, June.
    2. 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.
    3. Kneip, Alois & Park, Byeong U. & Simar, Léopold, 1998. "A Note On The Convergence Of Nonparametric Dea Estimators For Production Efficiency Scores," Econometric Theory, Cambridge University Press, vol. 14(6), pages 783-793, December.
    4. 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:

    1. Jean-Pierre Florens & Léopold Simar & Ingrid Van Keilegom, 2020. "Estimation of the Boundary of a Variable Observed With Symmetric Error," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(529), pages 425-441, January.
    2. Kuosmanen, Timo & Johnson, Andrew, 2017. "Modeling joint production of multiple outputs in StoNED: Directional distance function approach," European Journal of Operational Research, Elsevier, vol. 262(2), pages 792-801.
    3. 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.
    4. Kneip, Alois & Simar, Léopold & Van Keilegom, Ingrid, 2015. "Frontier estimation in the presence of measurement error with unknown variance," Journal of Econometrics, Elsevier, vol. 184(2), pages 379-393.
    5. 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.
    6. Kneip, A. & Simar, L. & Van Keilegom I., 2010. "Boundary estimation in the presence of measurement error with unknown variance," LIDAM Discussion Papers ISBA 2010046, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    7. Meister, Alexander, 2006. "Estimating the support of multivariate densities under measurement error," Journal of Multivariate Analysis, Elsevier, vol. 97(8), pages 1702-1717, September.

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