Statistical Modelling and Regression Structures Festschrift in Honour of Ludwig Fahrmeir |
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| Editor:
| Kneib, Thomas
Tutz, Gerhard |
| ISBN: | 978-3-7908-2412-4 |
| Publication Date: | Feb 2010 |
| Publisher: | Physica-Verlag
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| Imprint: | Physica |
| Book Format: | Hardback |
| List Price: | USD $109.99 |
Book Description:
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Thecollectedcontributionscontainedwithinthisbookhavebeenwrittenbyfriends andcolleaguestoacknowledgeLudwigFahrmeir''swidespreadandimportantimpact onStatisticsasascience,whilecelebratinghis65thBirthday. Asayoungstudent,LudwigstartedhiscareerasaMathematician,buthequickly turnedintoarisingandshiningstarwithintheGermanandinternationalStatistics community. HesoonobtainedbothhisPhDandhisHabilitationattheTechnical UniversityofMunich. AfterashortperiodasavisitingprofessorattheUniversity...
More DescriptionThecollectedcontributionscontainedwithinthisbookhavebeenwrittenbyfriends andcolleaguestoacknowledgeLudwigFahrmeir''swidespreadandimportantimpact onStatisticsasascience,whilecelebratinghis65thBirthday. Asayoungstudent,LudwigstartedhiscareerasaMathematician,buthequickly turnedintoarisingandshiningstarwithintheGermanandinternationalStatistics community. HesoonobtainedbothhisPhDandhisHabilitationattheTechnical UniversityofMunich. AfterashortperiodasavisitingprofessorattheUniversity ofDortmund,hereturnedtohishomelandBavariaandwasappointedFullProfessor ofStatisticsattheUniversityofRegensburg,attheageof32. Someyearslater,hemovedtothecapitalofBavariaandbecameProfessoratthe DepartmentofStatisticsattheUniversityofMunich. Hisappointmenthadsigni?cant impactontheDepartmentsince,soonafterhisarrival,Ludwigstartedaninitiative toestablishacollaborativeresearchcenteronthe"StatisticalAnalysisofDiscrete Structures. "Afterasuccessfulapplicationforinitialfunding,furtherfundingwas extendedseveraltimes,untiltheresearchcenterreachedthemaximumperiodfor fundingin2006. Duringthecompleteduration,Ludwigservedasaspeakerofthe researchcenterand-tociteoneofthe?nalreferees-"manageditinaneasyand ef?cientwayandcontributedseveralimportantresults. " Duringthelastfortyyears,Ludwig''sworkhashadtremendousimpactontheS- tisticscommunity. Hewasamongthe?rstresearcherstorecognizetheimportance ofgeneralizedlinearmodelsandcontributedinaseriesofpaperstothetheoretical backgroundofthatmodelclass. Hisinterestinstatisticalmodellingledtothe- ganizationofaworkshopon"StatisticalModellingandGeneralizedLinearModels (GLIM)"inMunichin1992andculminatedinthehighlycitedmonographon"M- tivariateStatisticalModellingBasedonGeneralizedLinearModels"thatsawtwo printingsandremainstobeakeyreferenceonappliedstatisticalmodellingutilizing generalizedlinearmodels. Ludwigalsohadgreatin?uenceonthecreationofthe StatisticalModellingSociety,andiscurrentlyontheadvisoryboardofthecor- spondingjournalon"StatisticalModelling. "Boththesocietyandjournalemerged outoftheearlyGLIMworkshopsandproceedings. v vi Foreword Ofcourse,Ludwig''sworkisde?nitelynotrestrictedtogeneralizedlinearmodels but-onthecontrary-spansawiderangeofmodernStatistics. Heco-authoredor co-editedseveralmonographs,e. g. onMultivariateStatistics,StochasticProcesses, MeasurementofCreditRisks,aswellaspopulartextbooksonRegressionandan IntroductiontoStatistics. Hisrecentresearchcontributionsaremostlyconcentrated insemiparametricregressionandspatialstatisticswithinaBayesianframework. When?rstcirculatingtheideaofaFestschriftforthecelebrationofLudwig''s 65thbirthday,allpotentialcontributorswereextremelypositive,manyimmediately agreeingtocontribute. ThesereactionsatesttoLudwig''shighpersonalandp- fessionalappreciationinthestatisticalcommunity. Thefarreachingandvarietyof subjectscoveredwithinthesecontributionsalsorepresentsLudwig''sbroadinterest andimpactinmanybranchesofmodernStatistics. BotheditorsofthisFestschriftwereluckyenoughtoworkwithLudwigatseveral occasionsandinparticularearlyintheircareersasPhDstudentsandPostDocs. His personalandprofessionalmentorshipandhisstrongcommitmentmadehimaperfect supervisorandhispatient,con?dentandencouragingworkingstylewillalwaysbe rememberedbyallofhisstudentsandcolleagues. Ludwigalwaysprovidedafriendly workingenvironmentthatmadeitapleasureandanhonortobeapartofhisworking group. WeareproudtobeabletosaythatLudwigismuchmorethanacolleague butturnedintoafriendforbothofus. OldenburgandMunich,January2010 ThomasKneib,GerhardTutz Acknowledgements Theeditorswouldliketoexpresstheirgratitudeto * allauthorsofthisvolumefortheiragreementtocontributeandtheireasyco- erationatseveralstagesofputtingtogetherthe?nalversionoftheFestschrift. * JohannaBrandt,JanGertheiss,AndreasGroll,FelixHeinzl,SebastianPetry,Jan UlbrichtandStephanieRubenbauerfortheirinvaluablecontributionsinproof- A readingandcorrectionofthepapers,aswellasinsolvingseveralLTX-related E problems. * theSpringerVerlagforagreeingtopublishthisFestschriftandinparticularNils- PeterThomas,AliceBlanck and FrankHolzwarthfor the smooth collabo- tion in preparing th emanuscript. vii Contents ListofContributors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix TheSmoothComplexLogarithmandQuasi-PeriodicModels . . . . . . . . . . 1 PaulH. C. Eilers 1 Foreword. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 3 DataandModels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3. 1 TheBasicModel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3. 2 SplinesandPenalties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3. 3 StartingValues. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3. 4 SimpleTrendCorrectionandPriorTransformation. . . . . 8 3. 5 AComplexSignal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3. 6 Non-normalDataandCascadedLinks. . . . . . . . . . . . . . . . 10 3. 7 AddingHarmonics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 4 MoretoExplore. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 5 Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 P-splineVaryingCoef?cientModelsforComplexData. . . . . . . . . . . . . . . . 19 BrianD. Marx 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2 "LargeScale"VCM,withoutBack?tting. . . . . . . . . . . . . . . . . . . . . . 22 3 NotationandSnapshotofaSmoothingTool:B-splines. . . . . . . . . . 24 3. 1 GeneralKnotPlacement. . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3. 2 SmoothingtheKTBData. . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4 UsingB-splinesforVaryingCoef?cientModels. . . . . . . . . . . . . . . . 26 5 P-splineSnapshot:Equally-SpacedKnots&Penalization. . . . . . . . 28 5. 1 P-splinesforAdditiveVCMs. . . . . . . . . . . . . . . . . . . . . . . . 30 5. 2 StandardErrorBands. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 6 OptimallyTuningP-splines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 7 MoreKTBResults. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 8 ExtendingP-VCMintotheGeneralizedLinearModel. . . . . . . . . . 33 9 Two-dimensionalVaryingCoef?cientModels. . . . . . . . . . . . . . . . . 36 ix x Contents 9. 1 Mechanicsof2D-VCMthroughExample . . . . . . . . . . . . . 37 9. 2 VCMsandPenaltiesasArrays. . . . . . . . . . . . . . . . . . . . . . . 39 9. 3 Ef?cientComputationUsingArrayRegression. . . . . . . . . 40 10 DiscussionTowardMoreComplexVCMs. . . . . . . . . . . . . . . . . . . . . 41 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 PenalizedSplines,MixedModelsandBayesianIdeas. . . . . . . . . . . . . . . . . . 45 ¨ GoranKauermann 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2 NotationandPenalizedSplinesasLinearMixedModels. . . . . . . . 46 3 Classi?cationwithMixedModels. . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4 VariableSelectionwithSimplePriors. . . . . . . . . . . . . . . . . . . . . . . . 50 4. 1 MarginalAkaikeInformationCriterion. . . . . . . . . . . . . . . 50 4. 2 ComparisoninLinearModels. . . . . . . . . . . . . . . . . . . . . . .