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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.

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Bibliographic Info

Article provided by Elsevier in its journal Statistics & Probability Letters.

Volume (Year): 68 (2004)
Issue (Month): 1 (June)
Pages: 39-49

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Handle: RePEc:eee:stapro:v:68:y:2004:i:1:p:39-49

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Related research

Keywords: Estimation of support of a probability density Deconvolution Extreme value distribution Optimal rates of convergence;

References

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  1. 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.
  2. Kneip, Alois & Park, Byeong U. & Simar, L opold, 1998. "A Note On The Convergence Of Nonparametric Dea Estimators For Production Efficiency Scores," Econometric Theory, Cambridge University Press, vol. 14(06), pages 783-793, December.
  3. 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.
  4. 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.
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