Tutorial -Quantile regression

《Tutorial -Quantile regression》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、TUTORIALONQUANTILEREGRESSIONXumingHeDepartmentofStatistics,UniversityofIllinoisatUrbana-ChampaignYingWeiDepartmentofBiostatistics,ColumbiaUniversityENAR2005TUTORIALONQUANTILEREGRESSION–p.1Motivationforquantileregression•Regression—toobtainasummaryoftherelationshipbetween

2、aresponsevariableyandasetofcovariatesx.•Leastsquaresregressioncaptureshowthemeanofychangeswithx.•Sometimes,asinglemeancurveisnotinformativeenough.•Conditionalquantilefunctionsprovideamorecompleteview.TUTORIALONQUANTILEREGRESSION–p.2Motivationforquantileregression0.90.75Y

3、Y0.50.90.250.7524680.10.50.250.10246810120.00.20.40.60.81.0X0.60.81.01.21.41.6XThedistributionofymaybeHeteroscedasticitymayexistasymmetricaroundtheinthedata.mean.TUTORIALONQUANTILEREGRESSION–p.3Example1–Riskfactorsforlowbirthweight•Lowbirthweightisknowntobeassociatedwith

4、◦higherinfantmortality(Abreveya,2001).◦higherhealth-carecost(Lewitetal.,1995).◦awiderangeofsubsequenthealthproblems(Hacketal.,1995).◦long-termeducationalattainmentandevenlabormarketoutcomes(CormanandChaikind,1998,andCurrieandHyson,1999).•Investigatethefactorsinfluencingbi

5、rthweight,especiallytheonesthatmayhelpreducetheincidenceoflowbirthweightinfants.TUTORIALONQUANTILEREGRESSION–p.4Example1–Riskfactorsforlowbirthweight•Theresearchquestioncanberephrasedasexploringthecovariateeffectsonthelowerquantilesofbirthweight.•Potentialcovariatesinclu

6、de◦Mother’seducation◦Mother’sprenatalcare◦Mother’sage◦Mother’sweightgain◦...•Covariateeffectsonlowerquantilesmaydifferfromthoseonthemeanormedianbirthweight.•Reference:Abreveya(2001)andKoenkerandHallock(2001).TUTORIALONQUANTILEREGRESSION–p.5Example2–Growthcharts95%75%50%2

7、5%•Displaythedistributionofa5%certainmeasurementwithinaWeight(kg)certainrangeoftimefora5101520certainpopulation.0.00.51.01.52.0AgeTUTORIALONQUANTILEREGRESSION–p.6Example2–Growthcharts95%•Usedtoscreenthe75%50%measurementsfroman25%individualsubjectintheB5%contextofpopulati

8、onvalues.Weight(kg)•Focusedontheentire5101520distribution,especiallytheAextremequantiles.0.00.51.01.52.