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Statistical Modelling and Regression Structures (eBook, PDF)

Festschrift in Honour of Ludwig Fahrmeir

Redaktion: Kneib, Thomas; Tutz, Gerhard

Beschreibung

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. . . . . . . . . . . . . . . . . . . . . . .

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Produktdetails

• Verlag: Physica-Verlag HD
• Seitenzahl: 472
• Erscheinungstermin: 12. Januar 2010
• Englisch
• ISBN-13: 9783790824131
• Artikelnr.: 37398939

Rezensionen

From the reviews:
"The festschrift is a collection of 24 contributions stemming from a wide area of statistical models ranging from semiparametric and geoadditive regression to Bayesian inference, time series modeling, statistical regularization, and others. The topics are of current interest. ... The format of the volume is uniform and nicely presented ... . will be a useful resource for graduate students, researchers, and practitioners with an interest in these topics. I think the festschrift deserves a broad readership." (Technometrics, Vol. 52 (3), August, 2010)