广义岭型主相关估计与可容许性的研究

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1、北京交通大学硕士学位论文广义岭型主相关估计与可容许性的研究姓名：郭文星申请学位级别：硕士专业：概率论与数理统计指导教师：张尚立20080501ABSTRACTABSTRACT：Theleastsquaresestimateoftheregressionparameters(shortenedformLSestimate)hasmany900dnature，forexample,whenerrorisnormallydistributioninregressionmodel，ithasthesmallestvarianceinallunbiasedestimatesclass．Bu

2、t，whenassumesXshowsstrangestate，bynOWalthoughitsvarianceisthesmallestinthelinearunbiasedestimateclass，butitsmeansquareserrorisveryactuallybig．Thereforemanyscholarsdevotetotheimprovementestimate，proposedmanynewestimates．averyimportantkindofestimatesisunbiasedestimates．Andinnumerousunbiasedesti

3、mates，whataffectsthebiggestistheridgeestimated，generalizedridgeestimate，principalcomponentsestimate，principalcorrelationestimateandSteinestimateandSOon．Inthispaper,weproposeanewbiasedestimateoftheregressionparameters--thegeneralizedridgeandprincipalcorrelationestimateinthethirdchapter,Wegivei

4、tssomepropertiesandprovethatitissuperiortoLSE(1eastsquaresestimate)，principalcorrelationestimate，ridgeandprincipalcorrelationestimateundersomecertainconditionswhenweselectMSE(meansquareserror)andPMC(pitmancloseness)criterionrespectively．Inthefourthchapter,promotesthegeneralizedridgeandprincip

5、—alingrowthcurvemodel．similarlyhadprovenitsoptimality,anditsoptimalityhasbeconfirmedthroughtheactualdata．Theadmissibilityisthemostminimumrequesttoanestimate．Inthefifthchapter,thispaperprovedtheprincipalcorrelationestimateisadmissible，andconsideringtheadmissibilityofLinearestimatesingrowthcurv

6、emodelundermatrixlosswithrespecttoanIncompleteEllipsoidalRestriction，weusethefactthattheadmissibilityoftheLinearestimateingrowthcurvemodelwithanRestrictionundermatrixlossisidenticalwiththatoftheLinearestimateinthenecessaryandsufficientsingleLinearmodelundermatrixloss．Fromthatweobtainthenecess

7、aryandsufficientconditionsforDYF+CtobeadmissibleestimatesofestimablefunctionKBLinthenon—homogenouslinearclass．KEYWORDS：Linearregressionmodel；GeneralizedridgeandprincipalcorrelationEstimate；Meansquareserror；Pitmanclosenesscriterion；growthcurve