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June 1996 Robust estimation of the location of a vertical tangent in distribution
R. V. Erickson
Ann. Statist. 24(3): 1423-1431 (June 1996). DOI: 10.1214/aos/1032526977


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.


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R. V. Erickson. "Robust estimation of the location of a vertical tangent in distribution." Ann. Statist. 24 (3) 1423 - 1431, June 1996.


Published: June 1996
First available in Project Euclid: 20 September 2002

zbMATH: 0862.62027
MathSciNet: MR1401858
Digital Object Identifier: 10.1214/aos/1032526977

Primary: 62F12
Secondary: 62E20

Keywords: asymptotic distribution , hyperefficient estimation , robust , singularity

Rights: Copyright © 1996 Institute of Mathematical Statistics

Vol.24 • No. 3 • June 1996
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