The Annals of Statistics

An Efficient and Robust Adaptive Estimator of Location

Rudolf Beran

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Abstract

A nonparametric minimum Hellinger distance estimator of location is introduced and shown to be asymptotically efficient at every symmetric density with finite Fisher information. Under small, possibly asymmetric, perturbations in such a density, the estimator is asymptotically robust in a technical sense which extends Hajek's concept of "regularity." A numerical example illustrates the computational feasibility of the estimator and its resistance to an arbitrary single outlier.

Article information

Source
Ann. Statist., Volume 6, Number 2 (1978), 292-313.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176344125

Digital Object Identifier
doi:10.1214/aos/1176344125

Mathematical Reviews number (MathSciNet)
MR518885

Zentralblatt MATH identifier
0378.62051

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation
Secondary: 62G35: Robustness

Keywords
Minimum Hellinger distance adaptive location estimator asymptotically efficient robust estimator nonparametric estimator contiguity

Citation

Beran, Rudolf. An Efficient and Robust Adaptive Estimator of Location. Ann. Statist. 6 (1978), no. 2, 292--313. doi:10.1214/aos/1176344125. https://projecteuclid.org/euclid.aos/1176344125


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