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June, 1988 Pathologies of some Minimum Distance Estimators
David L. Donoho, Richard C. Liu
Ann. Statist. 16(2): 587-608 (June, 1988). DOI: 10.1214/aos/1176350821

Abstract

Minimum distance estimates are studied at the $N(\theta, 1)$ model. Estimates based on a non-Hilbertian distance $\mu (\mu = \text{Kolmogorov-Smirnov, Levy, Kuiper, variation and Prohorov})$ can exhibit very large variances, or even outright inconsistency, at distributions arbitrarily close to the model in terms of $\mu$-distance. For Hilbertian distances $(\mu = \text{Cramer-von Mises, Hellinger})$ this problem does not seem to occur. Geometric motivation for these results is provided.

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David L. Donoho. Richard C. Liu. "Pathologies of some Minimum Distance Estimators." Ann. Statist. 16 (2) 587 - 608, June, 1988. https://doi.org/10.1214/aos/1176350821

Information

Published: June, 1988
First available in Project Euclid: 12 April 2007

zbMATH: 0684.62029
MathSciNet: MR947563
Digital Object Identifier: 10.1214/aos/1176350821

Subjects:
Primary: 62F35
Secondary: 62F12

Rights: Copyright © 1988 Institute of Mathematical Statistics

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Vol.16 • No. 2 • June, 1988
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