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非参和半参回归模型的稳健和截面推断.docx

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非参和半参回归模型的稳健和截面推断 Introduction Regressionanalysisiswidelyusedinvariousfieldstopredicttheoutcomeofadependentvariablebasedononeormoreindependentvariables.However,thestandardlinearregressionmodelhassomelimitations,suchastheassumptionofnormalityandhomoscedasticityoftheerrorterms.Insomecases,theseassumptionsmaynothold,leadingtobiasedorinefficientestimates.Therefore,researchersdevelopednonparametricandsemiparametricregressionmodelsthatrelaxsomeoftheseassumptions.Inthispaper,wediscusstherobustnessandcross-sectionalinferenceofnonparametricandsemiparametricregressionmodels. NonparametricRegressionModels Nonparametricregressionmodelsdonotassumeaparticularfunctionalformfortherelationshipbetweenthedependentandindependentvariables.Instead,theyestimatetherelationshipusingflexiblefunctionsthatfollowthedataclosely.Examplesofnonparametricregressionmodelsincludekernelregression,splineregression,andlocalpolynomialregression. Theadvantageofnonparametricregressionmodelsisthattheycancapturecomplexandnonlinearrelationshipsbetweenthevariableswithoutspecifyingafunctionalform.Additionally,theydonotrequirecertaindistributionalassumptions,makingthemrobusttodeviationsfromthenormalityassumption. Robustnessreferstotheabilityofastatisticalmethodtoprovidereliableestimatesevenwhensomeassumptionsareviolated.Nonparametricregressionmodelsaremorerobustthanparametricmodelsinthepresenceofoutliersorheavy-taileddistributions.However,theymaysufferfromthecurseofdimensionalitywhenthenumberofpredictorsincreases.Inthatcase,theymayneedalargesamplesizetoavoidoverfitting. SemiparametricRegressionModels Semiparametricregressionmodelscombinenonparametricandparametriccomponentstoestimatetherelationshipbetweenthevariables.Theyassumesomefunctionalformfortheparametriccomponentwhileallowingthenonparametriccomponenttoremainflexible.Examplesofsemiparametricregressionmodelsincludegeneralizedadditivemodels(GAMs)andpartiallylinearmodels(PLMs). Theadvantageofsemiparametricmodelsisthattheycancapturenonlinearitieswhilestilltaking