Page - 343 - in Differential Geometrical Theory of Statistics

Entropy2016,18, 421 16. Anaya-Izquierdo,K.;Critchley,F.;Marriott,P.;Vos,P.Onthegeometric interplaybetweengoodness-of-fit andestimation: Illustrativeexamples. InComputational InformationGeometry: For ImageandSignalProcessing; LectureNotes inComputerScience (LNCS);Nielsen, F.,Dodson,K.,Critchley, F., Eds.; Springer: Berlin, Germany,2016. 17. Morris,C.Central limit theoremsformultinomial sums.Ann. Stat. 1975,3, 165–188. 18. Osius,G.;Rojek,D.Normalgoodness-of-fit tests formultinomialmodelswith largedegreesof freedom. JASA1992,87, 1145–1152. 19. Holst,L.Asymptoticnormalityandefficiencyforcertaingoodness-of-fit tests.Biometrika1972,59, 137–145. 20. Koehler,K.J.;Larntz,K.Anempirical investigationofgoodness-of-fitstatistics forsparsemultinomials. JASA 1980,75, 336–344. 21. Koehler,K.J.Goodness-of-fit tests for log-linearmodels insparsecontingency tables. JASA1986, 81, 483–493. 22. McCullagh, P. The conditional distribution of goodness-of-fit statistics for discrete data. JASA 1986, 81, 104–107. 23. Forster, J.J.;McDonald, J.W.; Smith,P.W.F.MonteCarloexact conditional tests for log-linearand logistic models. J.R.Stat. Soc. B1996,58, 445–453. 24. Kim,D.;Agresti,A.Nearlyexact testsofconditional independenceandmarginalhomogeneity forsparse contingencytables.Comput. Stat.DataAnal. 1997,24, 89–104. 25. Booth, J.G.;Butler,R.W.Animportancesamplingalgorithmforexactconditional tests in log-linearmodels. Biometrika1999,86, 321–332. 26. Caffo,B.S.; Booth, J.G.MonteCarloconditional inference for log-linearand logisticmodels: Asurveyof currentmethodology.Stat.MethodsMed.Res. 2003,12, 109–123. 27. Lloyd,C.J.ComputinghighlyaccurateorexactP-valuesusingimportancesampling.Comput. Stat.DataAnal. 2012,56, 1784–1794. 28. Simonoff, J.S. Jackknifingandbootstrappinggoodness-of-fit statistics insparsemultinomials. JASA1986,81, 1005–1011. 29. Gaunt, R.E.; Pickett, A.; Reinert, G. Chi-square approximation by Stein’s method with application to Pearson’sstatistic. arXiv2015, arXiv:1507.01707. 30. Fan, J.; Hung, H.-N.; Wong, W.-H. Geometric understanding of likelihood ratio statistics. JASA 2000, 95, 836–841. 31. Ulyanov,V.V.; Zubov,V.N.Refinement on the convergence of one family of goodness-of-fit statistics to chi-squareddistribution.HiroshimaMath. J.2009,39, 133–161. 32. Asylbekov,Z.A.;Zubov,V.N.;Ulyanov,V.V.Onapproximatingsomestatisticsofgoodness-of-fit tests in the caseof three-dimensionaldiscretedata.Sib.Math. J.2011,52, 571–584. 33. Zelterman,D.Goodness-of-fit tests for largesparsemultinomialdistributions. JASA1987,82, 624–629. 34. Bregman,L.M.Therelaxationmethodoffindingthecommonpointofconvexsetsanditsapplication to the solutionofproblemsinconvexprogramming.USSRComp.Math.Math. 1967,7, 200–217. 35. Amari,S.-I. InformationGeometryandItsApplications; Springer: Tokyo, Japan,2015. 36. Csiszár, I.Ontopologicalpropertiesof f-divergences.Stud. Sci.Math.Hung. 1967,2, 329–339. 37. Csiszár, I. Informationmeasures: A critical survey. In Transactions of the Seventh Prague Conference on Information Theory, Statistical Decision Functions, Random Processes and of the 1974 European Meeting of Statisticians;Kozesnik, J.,Ed.;Springer:Houten,TheNetherlands,1977;VolumeB,pp. 73–86. 38. Barndorff-Nielsen, O. Information and Exponential Families in Statistical Theory; JohnWiley&Sons, Ltd.: Chichester,UK,1978. 39. Brown, L.D.Fundamentals of Statistical Exponential FamilieswithApplications in StatisticalDecisionTheory; LectureNotes-MonographSeries; IntegratedMediaSystems(IMS):Hayward,CA,USA,1986;Volume9. 40. Csiszár, I.;Matúš,F.Closuresofexponential families.Ann.Probab. 2005,33, 582–600. 41. Eriksson,N.;Fienberg,S.E.;Rinaldo,A.;Sullivant,S.Polyhedral conditions for thenonexistenceof theMLE forhierarchical log-linearmodels. J.Symb.Comput. 2006,41, 222–233. 343