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1、StatisticsandProbabilityLetters83(2013)61–69ContentslistsavailableatSciVerseScienceDirectStatisticsandProbabilityLettersjournalhomepage:www.elsevier.com/locate/staproVariableselectioninapartiallylinearproportionalhazardsmodelwithadivergingdimensionalityY
2、uaoHu,HengLian∗DivisionofMathematicalSciences,SPMS,NanyangTechnologicalUniversitySingapore,637371,SingaporearticleinfoabstractArticlehistory:WeconsidertheproblemofsimultaneousvariableselectionandestimationinpartiallyReceived25May2012linearproportionalhaz
3、ardsmodelswhenthenumberofcovariatesinthelinearpartReceivedinrevisedform27August2012divergeswiththesamplesize.Weapplythesmoothlyclippedabsolutedeviation(SCAD)Accepted28August2012penaltytoselectthesignificantcovariatesinthelinearpart.Somesimulationsandarea
4、lAvailableonline5September2012datasetarepresented.©2012ElsevierB.V.Allrightsreserved.Keywords:Akaikeinformationcriterion(AIC)Bayesianinformationcriterion(BIC)Cross-validationPartiallikelihoodSCAD1.IntroductionNowadays,moreandmoreresearchersareconcernedwi
5、thdataanalysistasksinwhichalargenumberofpredic-tors/featuresareused.Thisisduetothefactthat,inastudywheretherearelimitedpreviousexperiences,itishardtoidentifyasmallnumberofpredictorssuchthatitisbelievedthatonlythesevariablescontributetotheresponseofintere
6、st.Thusalargenumberofpredictorssuspectedtoberelatedtoresponsesneedtobecollectedtoavoidmodelmisspecification.Ontheotherhand,duetothelargenumberofpredictorscollected,itisdesirabletoselectasmallnumberofpredictorsthatarerelevantforprediction.Variableselectio
7、nisanimportantresearchtopicinmodernstatistics.Withalargenumberofpredictorsavailabletoincludeintothemodel,manyofthemmaynotberelevantforprediction,andinclusionoftheseonlyhurtsestimationperformance.Recently,therehasbeenconsiderableinterestininvestigatingthe
8、variableselectionproblemforparametricandnonparametricmodels.Traditionalvariableselectionmethodssuchasstepwiseregressionandbestsubsetselectionsufferfrominstability,asarguedinBreiman(1996),whichispartofthereasonwhyapenalizat
