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Entropy2016,18, 277 5. Chrétien,S.;Hero,A.O.Accelerationof theEMalgorithmviaproximalpoint iterations. InProceedingsof the IEEEInternationalSymposiumonInformationTheory,Cambridge,MA,USA,16–21August1998. 6. Csiszár, I. Eine informationstheoretischeUngleichungundihreanwendungaufdenBeweisderergodizität vonMarkoffschenKetten. Publ.Math. Inst.Hung.Acad. Sci. 1963,8, 95–108. (InGerman) 7. Broniatowski,M.;Keziou,A. Parametricestimationandtests throughdivergencesandtheduality technique. J.Multivar.Anal. 2009,100, 16–36. 8. Cressie,N.;Read,T.R.C.Multinomialgoodness-of-fit tests. J.R.Stat. Soc. Ser. B1984,46, 440–464. 9. Broniatowski,M.;Keziou,A.Minimizationofdivergencesonsetsofsignedmeasures. Stud. Sci.Math.Hung. 2006,43, 403–442. 10. Liese, F.; Vajda, I. OnDivergences and Informations in Statistics and InformationTheory. IEEETrans. Inf.Theory2006,52, 4394–4412. 11. AlMohamad,D. Towards abetter understandingof thedual representationof phi divergences. 2016, arXiv:1506.02166. 12. Toma,A.;Broniatowski,M.Dualdivergenceestimatorsandtests: Robustnessresults. J.Multivar.Anal. 2011, 102, 20–36. 13. Rockafellar,R.T.;Wets,R.J.B.VariationalAnalysis, 3rded.;Springer: Berlin/Heidelberg,Germany,1998. 14. Basu,A.;Harris, I.R.;Hjort,N.L.; Jones,M.C. Robust andEfficientEstimationbyMinimisingaDensity PowerDivergence. Biometrika1998,85, 549–559. 15. Dempster,A.P.;Laird,N.M.;Rubin,D.B.Maximumlikelihoodfromincompletedatavia theEMalgorithm. J.R.Stat. Soc. B1977,39, 1–38. 16. Wu,C.F.J. OntheConvergencePropertiesof theEMAlgorithm. Ann. Stat. 1983,11, 95–103. 17. Ostrowski,A. SolutionofEquationsandSystemsofEquations;AcademicPress:Cambridge,MA,USA,1966. 18. Chrétien,S.;Hero,A.O.OnEMalgorithmsandtheirproximalgeneralizations. ESAIMProbabil. Stat. 2008, 12, 308–326. 19. Berge,C.TopologicalSpaces: IncludingaTreatmentofMulti-valuedFunctions,VectorSpaces, andConvexity;Dover Publications:Mineola,NY,USA,1963. 20. Meister,A.DeconvolutionProblems inNonparametricStatistics; Springer: Berlin/Heidelberg,Germany,2009. 21. Jiménz,R.;Shao,Y. Onrobustnessandefficiencyofminimumdivergenceestimators. Test2001,10, 241–248. 22. Nelder, J.A.;Mead,R. ASimplexMethodforFunctionMinimization. Comput. J.1965,7, 308–313. 23. TheRCoreTeam. R:ALanguage andEnvironment for StatisticalComputing; RFoundation for Statistical Computing:Vienna,Austria,2013. c©2016bytheauthors. LicenseeMDPI,Basel,Switzerland. Thisarticle isanopenaccess articledistributedunder the termsandconditionsof theCreativeCommonsAttribution (CCBY) license (http://creativecommons.org/licenses/by/4.0/). 270
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Differential Geometrical Theory of Statistics
Titel
Differential Geometrical Theory of Statistics
Autoren
Frédéric Barbaresco
Frank Nielsen
Herausgeber
MDPI
Ort
Basel
Datum
2017
Sprache
englisch
Lizenz
CC BY-NC-ND 4.0
ISBN
978-3-03842-425-3
Abmessungen
17.0 x 24.4 cm
Seiten
476
Schlagwörter
Entropy, Coding Theory, Maximum entropy, Information geometry, Computational Information Geometry, Hessian Geometry, Divergence Geometry, Information topology, Cohomology, Shape Space, Statistical physics, Thermodynamics
Kategorien
Naturwissenschaften Physik
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Differential Geometrical Theory of Statistics