The Annals of Statistics

Robust estimation of the location of a vertical tangent in distribution

R. V. Erickson

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It is shown that the location of the set of $m + 1$ observations with minimal diameter, within local data, is a robust estimator of the location of a vertical tangent in a distribution function. The rate of consistency of these estimators is shown to be the same as that of asymptotically efficient estimators for the same model. Robustness means (1) only properties of the distribution local to the vertical tangent play a role in the asymptotics, and (2) these asymptotics can be proven given approximate information about just two parameters, the shape and quantile of the vertical tangent.

Article information

Ann. Statist., Volume 24, Number 3 (1996), 1423-1431.

First available in Project Euclid: 20 September 2002

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62F12: Asymptotic properties of estimators
Secondary: 62E20: Asymptotic distribution theory

Robust hyperefficient estimation singularity asymptotic distribution


Erickson, R. V. Robust estimation of the location of a vertical tangent in distribution. Ann. Statist. 24 (1996), no. 3, 1423--1431. doi:10.1214/aos/1032526977.

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  • 1 CHERNOFF, H. and RUBIN, H. 1956. The estimation of the location discontinuity in density. Proc. Third Berkeley Sy mp. Statist. Probab. 1 19 37. Univ. California Press, Berkeley.
  • 2 FEDERER, H. 1969. Geometric Measure Theory. Springer, New York.
  • 3 FELLER, W. 1971. An Introduction to Probability Theory and Its Applications, 2nd ed. Wiley, New York.
  • 4 HALL, P. 1982. On estimating the endpoint of a distribution. Ann. Statist. 10 556 568.
  • 5 IBRAGIMOV, I. A. and HAS'MINSKII, R. Z. 1981. Statistical Estimation Asy mptotic Theory Z. translated by Samuel Kotz. Springer, New York.
  • 6 STOUT, W. 1974. Almost Sure Convergence. Academic Press, New York.