26440.單指標(biāo)模型的高維懲罰經(jīng)驗(yàn)似然

1、單指標(biāo)模型的高維懲罰經(jīng)驗(yàn)似然專業(yè)名稱：概率論與數(shù)理統(tǒng)計(jì)申請(qǐng)人：李吉妮指導(dǎo)老師：張軍艦論文答辯委員會(huì)主席：氣M‘“t委員：PenalizedHighDimensionalEmpiricalLikelihoodforSingle—indexmodelsPostgraduate：LiJiniSupervisor：JunjianZhangSpecialty：Probabilitytheory＆MathematicalStatisticsRese

2、archFields：MathematicalStatisticsGrade：AbstractSingleindexmodelisaspecialkindofgeneralizedsemiparametricmodelandisaneffectivetoolfordealingwiththeproblemofmultivariatenonparametricregression，andiswidelyusedNearlytwodecad

3、es，variableselectionofhighdimensionaldatahasbecomeoneofthehotareasofstatisticsandrelatedresearchIndealingwithhigh—dimensionaldata，thedropingWittofsingleindexmodelnotonlyeffectivelyavoidthe“curseofdimensionality”problems，

4、butalsotoseizethepropertiesofsparsehighdimensionaldataTheuseofasingleindexmodeldiscussedarticleaboutvariableselectionmethodafteranotherbutmostareforparameterPisthedimensionofthefixedtimeHoweveLinmanyhighdimensionalvariab

5、leselection，theparameterdimensionPgenerallyincreasesasthesamplesizen，whileincreasesTherefore，inthispaper’weproposeasingleindexmodelrobustvariableselectionmethods：BasedontheSCAD(SmoothlyClippedAbsoluteDeviation)penaltyfun

6、ctionandempiricallikeli、hoodofpunishmentempiricallikelihoodUndercertainregularityconditions，wefoundthattheparameterPdimensionincreaseswiththesamplesizenincreasespunishingexperiencelikelihoodestimationOraclestillhasanatur

7、e，thatis，ifthetruesparsemodel，thentheprobabilitytendsto1，theexperienceseemstopunishnon’zeroparametersofthemodeltodeterminetheestimatedcontingentwithsparsityBasedontheresultsofpreviousresearchhasbeenonthebasisofacomprehen

8、siveanalysisofthesingleindexmodel，mainlyonhigh—dimensionalsingleindexmodelparameterestimationandtestingproblemsWemainlywithFan＆Peng(2004)thelikelihoodofpunishmentideasandHjort(2009)，Chen(2009)empiricallikelihoodthought，f

9、orasinglehighdimensionalindexmodelproposedpunishmentempiricallikelihoodmethodTheoreticalproofandsimulationresultsshowthatthevariablesintheselectionofasingleindexmodelprocessingandinspectionissues，empiricallikelihoodmetho