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1、SASGlobalForum2010StatisticsandDataAnalysisPaper268-2010BootstrapMania!:Re-SamplingtheSAS®WayDavidL.Cassell,DesignPathways,Corvallis,ORABSTRACTThemostcommonwaythatpeopledosimulationsandre-samplingplansinSAS®is,infact,theslowandawkwardway.Peopletendtothinkintermsofahugemacroloopwrappedaro
2、undapieceofSAScode,withadditionalchunksofcodetogettheoutputsofinterestandthentoweldtogetherthepiecesfromeachiteration.ButSASisdesignedtoworkwithby-processing,sothereisafaster,cleaner,simplerway.Thebasicsofthisapproachhaveappearedinpreviouspapers,butthispaperfocusesonnewinnovationsinboots
3、trapping,andcodeforbootstrapmethodologieswhichhavenotbeenshownbefore.INTRODUCTIONThemostcommonwaythatpeoplebootstrapparameterestimatesinSASisthewaythatcausesmanypeopletoabandonSASforthissortoftask.Sofirst,whatisabootstrap,andhowdoweperformit?Forourpurposes,resamplingcoversarangeofideas.A
4、lloftheminvolvetakingoursampleandusingitasourbasisfordrawingnewsamples.Hencethename‘resampling’.Wesamplefromoursample,inonewayoranother.Thereareseveralwaysinwhichwecan‘resample’.Wecandraw‘randomly’fromoursample,orwecandrawdesignedsubsetsfromoursample.(Seeourdiscussionsonbootstrappingandj
5、ackknifingandcross-validation.)Also,wecanpullthedatabutexchangethelabelsonthedatapoints.(Seeourdiscussiononrandomizationtests.)Inbootstrapping,wewanttoapproximatetheentiresamplingdistributionofsomeestimator.Wecandothatbyresampling(simplerandomsamplingwithreplacement)fromouroriginalsample
6、.Typicallyinbootstrapping,wewanttoestimatethebiasoftheestimator,oritsstandarderror,oraconfidenceintervalfortheparameter.Bootstrappingisanon-parametricmethod,sincewearenotmakingspecificassumptionsaboutthedistribution(s)fromwhichthedataarise.Butthatdoesnotmeanthatithasnounderlyingassumptio
7、nsatall!Thisnon-parametricmethodologymeansthatbootstrappingcanbeausefulalternativetoinferencebasedon‘parametric’assumptions,forexample,inferencebasedonthenormalityofthedistributionoftheparameterestimates.Ifthetraditionalunderlyingassumptionsarenotmet,oraresuspect,thenanon
