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分位数变系数模型基于核光滑的变量选择(英文).docx

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分位数变系数模型基于核光滑的变量选择(英文) Introduction Quantileregressionisastatisticalmethodthatanalyzestherelationshipbetweenaresponsevariableandasetofindependentvariablesatdifferentquantilesoftheresponsevariabledistribution.Intraditionallinearregression,theaimistomodeltheconditionalmeanoftheresponsevariablegiventheindependentvariables.However,inmanyreal-worldscenarios,theconditionalmeanmaynotadequatelycapturethedistributionalpropertiesoftheresponsevariable.Quantileregressioncircumventsthisproblembymodelingtherelationshipbetweentheindependentvariablesanddifferentquantilesoftheresponsevariabledistribution,providingamorecomprehensiveunderstandingoftherelationship. Thecoefficientofvariationisameasureoftherelativespreadordispersionofaprobabilitydistribution.Itisdefinedastheratioofthestandarddeviationtothemeanofthedistribution.Thecoefficientofvariationiscommonlyusedinmanyfields,suchasfinance,ecology,andstatistics,tocomparethevariabilityofdifferentdistributions.Thecoefficientofvariationcanalsobeusedtomeasuretheheterogeneityofapopulation,whereahighercoefficientofvariationindicateshighervariabilityamongtheobservations. Inthispaper,weintroducethequantileregression-basedcoefficientofvariationmodel.Weproposeamethodforvariableselectionusingkernelsmoothingtoselectrelevantindependentvariablesthatcontributetothecoefficientofvariation.Inaddition,weprovideanexampleapplicationoftheproposedmodeltoareal-worlddataset. QuantileRegression Quantileregressionisanon-parametricregressiontechniquethatestimatestherelationshipbetweentheindependentvariablesanddifferentquantilesoftheresponsevariabledistribution.Themethodisparticularlyusefulwhentheconditionalmeanmaynotcapturethedistributionalpropertiesoftheresponsevariable.Thestandardquantileregressionmodelcanbewrittenas: Q(y|x)=x*β(t) whereQ(y|x)isthetthquantileoftheresponsevariableygiventheindependentvariablesx,β(t)isavectorofcoefficientsforthetthquantile,andxisamatrixofindependentvariables. Thequantileregressionmodelcanbeestimatedusingvarioustechniques,suchasthe