Page - 270 - in Differential Geometrical Theory of Statistics
Image of the Page - 270 -
Text of the Page - 270 -
Entropy2016,18, 277
5. Chrétien,S.;Hero,A.O.Accelerationof theEMalgorithmviaproximalpoint iterations. InProceedingsof
the IEEEInternationalSymposiumonInformationTheory,Cambridge,MA,USA,16â21August1998.
6. Csiszår, I. Eine informationstheoretischeUngleichungundihreanwendungaufdenBeweisderergodizitÀt
vonMarkoffschenKetten. Publ.Math. Inst.Hung.Acad. Sci. 1963,8, 95â108. (InGerman)
7. Broniatowski,M.;Keziou,A. Parametricestimationandtests throughdivergencesandtheduality technique.
J.Multivar.Anal. 2009,100, 16â36.
8. Cressie,N.;Read,T.R.C.Multinomialgoodness-of-ïŹt tests. J.R.Stat. Soc. Ser. B1984,46, 440â464.
9. Broniatowski,M.;Keziou,A.Minimizationofdivergencesonsetsofsignedmeasures. Stud. Sci.Math.Hung.
2006,43, 403â442.
10. Liese, F.; Vajda, I. OnDivergences and Informations in Statistics and InformationTheory. IEEETrans.
Inf.Theory2006,52, 4394â4412.
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, 20â36.
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 andEfïŹcientEstimationbyMinimisingaDensity
PowerDivergence. Biometrika1998,85, 549â559.
15. Dempster,A.P.;Laird,N.M.;Rubin,D.B.Maximumlikelihoodfromincompletedatavia theEMalgorithm.
J.R.Stat. Soc. B1977,39, 1â38.
16. Wu,C.F.J. OntheConvergencePropertiesof theEMAlgorithm. Ann. Stat. 1983,11, 95â103.
17. Ostrowski,A. SolutionofEquationsandSystemsofEquations;AcademicPress:Cambridge,MA,USA,1966.
18. Chrétien,S.;Hero,A.O.OnEMalgorithmsandtheirproximalgeneralizations. ESAIMProbabil. Stat. 2008,
12, 308â326.
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. JimĂ©nz,R.;Shao,Y. OnrobustnessandefïŹciencyofminimumdivergenceestimators. Test2001,10, 241â248.
22. Nelder, J.A.;Mead,R. ASimplexMethodforFunctionMinimization. Comput. J.1965,7, 308â313.
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
Differential Geometrical Theory of Statistics
- Title
- Differential Geometrical Theory of Statistics
- Authors
- Frédéric Barbaresco
- Frank Nielsen
- Editor
- MDPI
- Location
- Basel
- Date
- 2017
- Language
- English
- License
- CC BY-NC-ND 4.0
- ISBN
- 978-3-03842-425-3
- Size
- 17.0 x 24.4 cm
- Pages
- 476
- Keywords
- Entropy, Coding Theory, Maximum entropy, Information geometry, Computational Information Geometry, Hessian Geometry, Divergence Geometry, Information topology, Cohomology, Shape Space, Statistical physics, Thermodynamics
- Categories
- Naturwissenschaften Physik