The Annals of Statistics

Robust estimation of the location of a vertical tangent in distribution

R. V. Erickson

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 20 September 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1032526977

Digital Object Identifier
doi:10.1214/aos/1032526977

Mathematical Reviews number (MathSciNet)
MR1401858

Zentralblatt MATH identifier
0862.62027

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

Keywords
Robust hyperefficient estimation singularity asymptotic distribution

Citation

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. https://projecteuclid.org/euclid.aos/1032526977


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References

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