含缺失數(shù)據(jù)的線性模型回歸系數(shù)的約束EM算法.pdf

1、南京航空航天大學(xué)碩士學(xué)位論文含缺失數(shù)據(jù)的線性模型回歸系數(shù)的約束EM算法姓名：沈啟霞申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：計(jì)算數(shù)學(xué)指導(dǎo)教師：劉心聲20070301含缺失數(shù)據(jù)線性模型回歸系數(shù)的約束EM算法iiAbstractOneofthemostpowerfulalgithmsfobtainingmaximumlikelihoodestimatesfmanyincompletedataproblemsistheEMalgithm.Itisanitera

2、tivemethodtherearetwostepsineveryiterationoftheEMalgithm:oneiscalledEstepwhichistofindaconditionalexpectationbasedonaconditionaldistributiontheotheriscalledMstepwhichistofindamaximumlikelihoodestimat(MLE)basedonthecomple

3、tedataproblem.TherestrictedEMalgithmfmaximumlikelihoodestimationunderlinearequalitiesrestrictionsontheparametershasbeensolved.HoweverwhentheparameterssatisfyasetoflinearnonlinearinequalitiesrestrictionstheEMalgithmmaybet

4、oocomplicatedtoapplydirectly.ThispaperisdevotedtogivetherestrictedEMalgithmfregressioncoefficientsofthelinearmodelwithmissingdataheretheconstraintsaregivenbylinearnonlinearinequalitiesrespectively.Fthelinearrestrictionso

5、ntheparameterswegivetwoalgithmsthefirstismodifiedprojectionalgithmofKudoDykstra’sthisalgithmisappliedtoMstepofEMalgithmftwodimensionalnmaldistribution.TheotheroptimalalgithmofMstepistheHildrethD’Esopoalgithmsomeconvergen

6、cepropertiesoftheEMsequencearediscussed.fthenonlinearrestrictionsontheparametersbyusingtheasymptoticnmalityofthemaximumlikelihoodestimatswechangethiskindofestimationproblemtoastochasticoptimizationproblemintheMstepgiveth

7、elimitproblemofthestochasticoptimizationproblem.Thatiswegettheoptimalsolutionofthestochasticoptimizationproblembyusingthelimitproblemwhoseoptimalsolutioniseasilycomputedprovethattheoptimalsolutionofthestochasticoptimizat

8、ionproblemisconvergetotheoptimalsolutionofthelimitprobleminprobability.Finallythesuggestedalgithmsareillustratedbynumericalexamples.Keywds:IncompletedataEMalgithmMaximumlikelihoodestimatsLinearinequalitiesconstraintsLine