Cox比例風險模型的橋估計.pdf

1、遼寧師范大學碩士學位論文Cox比例風險模型的橋估計姓名：侯向艷申請學位級別：碩士專業(yè)：概率論與數理統(tǒng)計指導教師：侯文201204Cox比例風險模型的橋估計BridgeEstimatorforCox’SProportionalHazardModelAbstractWeinvestigatethevariableselectionproblemforCox’Sproportionalhazardsmodel，andproposeaunifi

2、edmodelselectionandestimationprocedurewithdesiredtheoreticalpropertiesandcomputationalconvenienceThenewmethodisbasedonapenalizedlogpartiallikelihoodwiththebridgepenaltyonregressioncoefficientsWeproposebridgeestimatorinCo

3、x’Sproportionalhazardmodelforparameterestimationandvariableselection(ie，todistinguishbetweencovariateswhosecoefficientsareexactlyzeroandcovariateswhosecoefficientsarenonzero)Underreasonableconditionstheconsistencyofthebr

4、idgeestimatorcanbeachievedFurthermore，itcanselectthenonzerocoefficientswithaprobabilityconvergingto1andtheestimatorsofnonzerocoefficientshavetheasymptoticnormality，namelytheoraclepropertyThispaperhasthefollowingseveralch

5、apters：Chapter1ismainlyintroducestheformofCoxproportionalhazardsmethodandthedefinitionofpenaltyfunctions，theformofpartiallikelihoodmethodandmangvariableselectedmethodsCorrespondingtothekindsofpenalizedfunctions，wepropose

6、thescholarsathomeandabroadonthebasisofresearchachievementsInthesecondofchapter，wegivethedefinitionofpenalizedpartiallikelihoodfunctionviabridgeestimatorisPy，。(夕)=粵。(∥)一胛f∑惻，basedonthedefinitionofpenalizedpartiallikelihoo

7、dfunctionviaLASSO，，。(∥)：粵。(∥)一聆f蘭圳，：lUnderreasonableconditions，weshowthatpenalizedempiricallikelihoodCanselectthenonzerocoefficientswithaprobabilityconvergingto1andtheestimatorsofnonzerocoefficientshavetheasymptoticnorma

8、lityAlltheproofsaregiveninthechapter3Lagrangemultipliermethod，centrallimittheoremandthemethodonestimationoftheorderofrandomvariablesisappliedtotheproofofthetheoremsintheprocessInchapter4outlinescomputationalaspectofbridg