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Convergence in distribution of minimum-distance estimators


Bolthausen, E (1977). Convergence in distribution of minimum-distance estimators. Metrika, 24(4):215-227.

Abstract

It is shown that (under some regularity conditions) minimum distance estimators for a (possibly multidimensional) real parameter of a family of univariate continuous distribution functions have an asymptotic distribution. If the distance is derived from the mean-square norm it is proved that the asymptotic distribution is normal. Weak convergence of empirical distribution to the Brownian bridge is the essential tool for the proof.

Abstract

It is shown that (under some regularity conditions) minimum distance estimators for a (possibly multidimensional) real parameter of a family of univariate continuous distribution functions have an asymptotic distribution. If the distance is derived from the mean-square norm it is proved that the asymptotic distribution is normal. Weak convergence of empirical distribution to the Brownian bridge is the essential tool for the proof.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Minimum-Distance Estimators; Convergence in Distribution; Skorohod Metric
Language:English
Date:1977
Deposited On:19 Oct 2009 14:21
Last Modified:05 Apr 2016 13:30
Publisher:Springer
ISSN:0026-1335
Free access at:Related URL. An embargo period may apply.
Publisher DOI:https://doi.org/10.1007/BF01893411
Related URLs:http://www.digizeitschriften.de/dms/img/?PPN=PPN358794056_0024&DMDID=dmdlog57
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0396.62022

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