The Annals of Statistics

Minimum Hellinger Distance Estimates for Parametric Models

Rudolf Beran

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Abstract

This paper defines and studies for independent identically distributed observations a new parametric estimation procedure which is asymptotically efficient under a specified regular parametric family of densities and is minimax robust in a small Hellinger metric neighborhood of the given family. Associated with the estimator is a goodness-of-fit statistic which assesses the adequacy of the chosen parametric model. The fitting of a normal location-scale model by the new procedure is exhibited numerically on clear and on contaminated data.

Article information

Source
Ann. Statist., Volume 5, Number 3 (1977), 445-463.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176343842

Digital Object Identifier
doi:10.1214/aos/1176343842

Mathematical Reviews number (MathSciNet)
MR448700

Zentralblatt MATH identifier
0381.62028

JSTOR
links.jstor.org

Subjects
Primary: 62G35: Robustness
Secondary: 62F10: Point estimation

Keywords
Robust estimates minimum Hellinger distance estimates asymptotically efficient estimates minimax robust

Citation

Beran, Rudolf. Minimum Hellinger Distance Estimates for Parametric Models. Ann. Statist. 5 (1977), no. 3, 445--463. doi:10.1214/aos/1176343842. https://projecteuclid.org/euclid.aos/1176343842


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