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Statements

Subject Item
n2:RIV%2F61989100%3A27510%2F14%3A86091093%21RIV15-MSM-27510___
rdf:type
skos:Concept n15:Vysledek
dcterms:description
Statistical inference can be interpreted as a problem of minimum distance between an empirical (observed) and a theoretical distribution. The most used measures of dissimilarity/disparity between probability distributions are the well known divergence measures. These measures are not symmetric: basing on the duality in their formulation, we classify divergences within the context of estimation into two main classes and analyze them with reference to majorization theory. In this regard, the consistency of divergence measures with respect to the generalized (strong) majorization pre-order is can be easily derived from a well known characterization theorem. Nevertheless, in many practical contexts such as estimation problem, one of the main assumption for (strong) majorization could be unfulfilled. Thus we study under which conditions divergence measures are consistent with respect to the generalization of weak majorization (from above). This paper provides a guideline for the choice of an appropriate divergence measure for minimum distance estimation purpose. The results hold for discrete probability distributions but can be easily generalized to positive measures and applied to many dissimilarity indices. Statistical inference can be interpreted as a problem of minimum distance between an empirical (observed) and a theoretical distribution. The most used measures of dissimilarity/disparity between probability distributions are the well known divergence measures. These measures are not symmetric: basing on the duality in their formulation, we classify divergences within the context of estimation into two main classes and analyze them with reference to majorization theory. In this regard, the consistency of divergence measures with respect to the generalized (strong) majorization pre-order is can be easily derived from a well known characterization theorem. Nevertheless, in many practical contexts such as estimation problem, one of the main assumption for (strong) majorization could be unfulfilled. Thus we study under which conditions divergence measures are consistent with respect to the generalization of weak majorization (from above). This paper provides a guideline for the choice of an appropriate divergence measure for minimum distance estimation purpose. The results hold for discrete probability distributions but can be easily generalized to positive measures and applied to many dissimilarity indices.
dcterms:title
Divergence measures and weak majorization in estimation problems Divergence measures and weak majorization in estimation problems
skos:prefLabel
Divergence measures and weak majorization in estimation problems Divergence measures and weak majorization in estimation problems
skos:notation
RIV/61989100:27510/14:86091093!RIV15-MSM-27510___
n3:aktivita
n16:P
n3:aktivity
P(EE2.3.30.0016)
n3:dodaniDat
n12:2015
n3:domaciTvurceVysledku
Lando, Tommaso
n3:druhVysledku
n4:D
n3:duvernostUdaju
n18:S
n3:entitaPredkladatele
n10:predkladatel
n3:idSjednocenehoVysledku
11899
n3:idVysledku
RIV/61989100:27510/14:86091093
n3:jazykVysledku
n11:eng
n3:klicovaSlova
dissimilarity; inequality; convex function; estimation; divergence measure; majorization
n3:klicoveSlovo
n7:inequality n7:majorization n7:divergence%20measure n7:dissimilarity n7:estimation n7:convex%20function
n3:kontrolniKodProRIV
[029E7E358825]
n3:mistoKonaniAkce
Gdaňsk
n3:mistoVydani
Cambridge
n3:nazevZdroje
Proceedings of the 2nd International Conference on Mathematical, Computational and Statistical Sciences (MCSS '14); Proceedings of the 7th International Conference on Finite Difference...: Gdansk, Poland May 15-17, 2014
n3:obor
n14:BB
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
2
n3:projekt
n6:EE2.3.30.0016
n3:rokUplatneniVysledku
n12:2014
n3:tvurceVysledku
Bertoli-Barsotti, Lucio Lando, Tommaso
n3:typAkce
n19:WRD
n3:zahajeniAkce
2014-05-25+02:00
s:issn
2227-4588
s:numberOfPages
6
n17:hasPublisher
WSEAS Press
n20:isbn
978-960-474-380-3
n9:organizacniJednotka
27510