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Entropy2016,18, 386 154. Bini,D.A.;Garoni,C.; Iannazzo,B.;Capizzano,S.S.; Sesana,D.AsymptoticBehaviourandComputationof Geometric-LikeMeansofToeplitzMatrices,SLA14Conference,Kalamata,Greece,September2014;Available online: http://noether.math.uoa.gr/conferences/sla2014/sites/default/ïŹles/Iannazzo.pdf (accessedon 8–12September2014). 155. Bini, D.A.; Garoni, C.; Iannazzo, B.; Capizzano, S.S. Geometricmeans of toeplitzmatrices by positive parametrizations. 2016, inpress. 156. Calvo,M.;Oller, J.M.Anexplicit solutionof informationgeodesicequations for themultivariatenormal model.Stat.Decis. 1991,9, 119–138. [CrossRef] 157. Calvo,M.;Oller, J.M.Adistancebetweenmultivariatenormaldistributionsbased inanembedding into the Siegelgroup. J.Multivar.Anal.Arch. 1990,35, 223–242. [CrossRef] 158. Calvo,M.;Oller, J.M.Adistancebetweenelliptical distributionsbased in anembedding into theSiegel group. J.Comput.Appl.Math. 2002,145, 319–334. [CrossRef] 159. Chevallier,E.;Barbaresco,F.;Angulo, J.Probabilitydensityestimationonthehyperbolic spaceappliedto radarprocessing. InGeometricScienceof InformationProceedings;LectureNotes inComputerScience;Springer: Berlin/Heidelberg,Germany,2015;Volume9389,pp.753–761. 160. Chevallier,E.;Forget,T.;Barbaresco,F.;Angulo, J.KernelDensityEstimationontheSiegelSpaceApplied toRadarProcessing.Availableonline: https://hal-ensmp.archives-ouvertes.fr/hal-01344910/document (accessedon24October2016). 161. Costa, S.I.R.; Santosa, S.A.; Strapasson, J.E. Fisher information distance: A geometrical reading. Discret. Appl.Math.2015,197, 59–69. [CrossRef] 162. Jeuris, B.; Vandebril, R.; Vandereycken, B. A survey and comparison of contemporary algorithms for computingthematrixgeometricmean.Electron. Trans.Numer.Anal. 2012,39, 379–402. 163. Jeuris, B. RiemannianOptimization forAveragingPositiveDeïŹniteMatrices. Ph.D. Thesis, Katholieke UniversiteitLeuven,Leuven,Belgium,2015. 164. Jeuris,B.;Vandebril,R.TheKĂ€hlerMeanofBlock-ToeplitzMatriceswithToeplitzStructuredBlocks;Department ofComputerScience,KULeuven: Leuven,Belgium,2015. 165. Maliavin, P. Invariant or quasi-invariant probabilitymeasures for inïŹnite dimensional groups, Part II: UnitarizingmeasuresorBerezinianmeasures. Jpn. J.Math. 2008,3, 19–47. [CrossRef] 166. Strapasson, J.E.; Porto, J.P.S.; Costa, S.I.R.Onbounds for the Fisher-Raodistance betweenmultivariate normaldistributions.AIPConf. Proc. 2015,1641, 313–320. 167. Hua, L.K.HarmonicAnalysis of Functions of Several ComplexVariables in the ClassicalDomains; American MathematicalSociety: Providence,RI,USA,1963. 168. Siegel,C.L.Symplecticgeometry.Am. J.Math. 1943,65, 1–86. [CrossRef] 169. Yoshizawa,S.;Tanabe,K.DualdifferentialgeometryassociatedwiththeKullback-Leibler informationon theGaussiandistributionsandits2-parametersdeformations.SUTJ.Math. 1999,35, 113–137. 170. Skovgaard, L.T.ARiemannianGeometry of theMultivariateNormalModel; Technical Report for Stanford University: Stanford,CA,USA,April1981. 171. Deza,M.M.;Deza,E.EncyclopediaofDistances, 3rded.;Springer: Berlin/Heidelberg,Germany,2013;p.242. 172. Casalis,M.Famillesexponentiellesnaturelles invariantesparungroupedetranslations.C.R.Acad. Sci. Ser. IMath. 1988,307, 621–623. (InFrench) 173. Casalis,M.FamillesExponentiellesNaturellesInvariantesparunGroupe. Ph.D.Thesis,ThĂšsedel’UniversitĂ© PaulSabatier,Toulouse,France,1990. (InFrench) 174. Casalis,M.Familles exponentiellesnaturelles sur rd invariantesparungroupe. Int. Stat. Rev. 1991, 59, 241–262. (InFrench) [CrossRef] 175. Casalis,M.Les famillesexponentiellesĂ variancequadratiquehomogĂšnesontdes loisdeWishart surun cĂŽnesymĂ©trique.C.R.Acad. Sci. Ser. IMath. 1991,312, 537–540. (InFrench) 176. Casalis,M.;Letac,G.Characterizationof theJĂžrgensenset ingeneralizedlinearmodels.Test1994,3, 145–162. [CrossRef] 177. Casalis,M.;Letac,G.TheLukacs-Olkin-Rubincharacterizationof theWishartdistributionsonsymmetric cone.Ann. Stat. 1996,24, 763–786. [CrossRef] 178. Casalis,M.The2d+4simplequadraticnaturalexponential familiesonRd.Ann. Stat. 1996,24, 1828–1854. 179. Letac,G.Acharacterizationof theWishartexponential familiesbyaninvarianceproperty. J.Theor. Probab. 1989,2, 71–86. [CrossRef] 117
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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