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Bootstrap and Monte Carlo.doc

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KeyideasofbootstrapsamplingBootstrapsamplingissamplingwithreplacement.Howtodothat?Supposeyoursamplecontainonly5observations.Youlabelyourobservationinto5ballswithnameABCDEPutallthe5ballsonabasket.Thenfromthese5ballsyoudraw1ballrandomlyandrecordthename.Afteryourecorditputbackthisballinthebasket.Makesurethatyoureturntheballinthebasketbeforemakinganotherrandomdraw.Thisissamplingwithreplacement.Repeattheworkofdrawanotherballrandomlyrecordthelabelandputbacktheballtothebasketuntilthousandoftime.Therecordedlabelsarecalledbootstrapsampling.Yougottheidea!Quitesimpleisn'tit?Yourrecordmaylooklikethis…..DEEABCBAEetc.Noticethatbecauseyoudrawwithreplacementbootstrapsamplingwillrepeatagainandagain.ThisisthepropertiesofBootstrapsampling.WhydoIneedBoostrapSampling?Iftheideaofbootstrapsamplingissosimplewhydoweneedtodobootstrapsampling?Fromasampleyoucanonlygetonestatisticforexamplemean.Youdonotknowtheconfidenceintervalofthismeanordistributionofthismean.Bootstrapsamplegivemoredetailonthedistributionofthismeanorprobabilityofthismean.ExampleinMSexcelbelowwillgiveyoubetterunderstandontheapplication.HowtodothatinMSExcel?Thissectionofthetutorialwillgiveyouthedetailonhowtodothat.Downloadtheworksheetexamplecompanionofthistutorialhere.TheExcelfilescontainnomacroonlypurespreadsheet.Supposewehave30dataoforiginalsamplethatwetakefromanobservationorexperimentsorquestionnairesurvey.Weputthisdatainseveralrowssothatwecanseethem.1.SelecttheregionoforiginalsampleandusemenuInsert–Name–Defineandtype“sample”totheoriginalsampleandclickOKbutton.2.InanyothercellbelowthisoriginalsamplesaycellB10type=INDEX(SampleROWS(Sample)*RAND()+1COLUMNS(Sample)*RAND()+1)