## The Annals of Statistics

### Robust estimation of the location of a vertical tangent in distribution

R. V. Erickson

#### 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

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

#### 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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