ln2 Review of Asymptotic Theory.pdf

ln2 Review of Asymptotic Theory.pdf

ID:33830707

大?。?74.13 KB

頁數(shù):20頁

時間:2019-03-01

ln2 Review of Asymptotic Theory.pdf_第1頁
ln2 Review of Asymptotic Theory.pdf_第2頁
ln2 Review of Asymptotic Theory.pdf_第3頁
ln2 Review of Asymptotic Theory.pdf_第4頁
ln2 Review of Asymptotic Theory.pdf_第5頁
資源描述:

《ln2 Review of Asymptotic Theory.pdf》由會員上傳分享,免費在線閱讀,更多相關(guān)內(nèi)容在學術(shù)論文-天天文庫

1、ApEc8212EconometricsAnalysis---Lecture#2ReviewofAsymptoticTheory(Wooldridge,Chap.3)Thislecturereviewsbasicresultsinasymptotictheory,whichmostofyouhaveseenbeforeinsomeform(Chapter4andAppendixDofGreene,2008).Thismaterialisnotveryexciting,butitisveryuseful.Wooldridgedoesnotgiveproofs,b

2、utyoucanseeGreene,andmoregenerallyHalbertWhite(2001,AsymptoticTheoryforEconometricians:RevisedEdition)forproofsandamorerigoroustreatment.I.ConvergenceofDeterministicSequencesLet’sstartwithsomedefinitions:Convergence:Asequenceof(nonrandom)numbers{aN:N=1,2,…}convergestoaif,forallε>0th

3、ereexistsanNεsuchthatifN>Nεthen

4、aN–a

5、<ε.ThisiswrittenasaN→aasN→∞,oraslimaN=a.N??Boundedness:Asequenceof(nonrandom)numbers{aN:N=1,2,…}isboundedifandonlyifthereissomeb<∞suchthat

6、aN

7、

8、λnumbersisatmostoforderN,denotedbyO(N),ifλaN/Nisbounded.Asequence{aN}isoforderλλλsmallerthanN,denotedbyo(N),iflimaN/N=0.N??Thesetwodefinitionsformalizewhatismeantby“thesameorderofmagnitude”anda“smallerorderλofmagnitude”.If{aN}isO(N),thenaNcannotbeλλinfinitelylargerthanNasN→∞.If{aN}i

9、so(N),λthenaNisinfinitelysmallerthanNasN→∞.Bothtypesoforderstatisticscanbeusedwithλ=0,inλλwhichcaseN=1.InthiscaseO(N)(“atmostoforder”)isdenotedasO(1),whichsimplymeansthatλ{aN}isbounded.Similarly,o(N)(“ofordersmallerthan”)isdenotedaso(1)whenλ=0,whichmeansthataNconvergestozero,i.e.lim

10、aN=0?{aN}iso(1).N??λλNotethatforanysequence{aN},o(N)impliesO(N):λλiflimaN/N=0thenaN/Nisbounded.Settingλ=0N??showsthatif{aN}convergesto0then{aN}isbounded.Finally,forsequencesofvectorsormatrices,theλsequenceisO(N)onlyifalltheelementsinitareλλO(N),andthesameholdsforo(N).2II.Convergence

11、inProbabilityandBoundedinProbability(op(1)andOp(1))Sofarwehavediscussedsequencesofnumbers,butineconometricsweworkwithvariables,soweneedtodefineboundednessandconvergenceofvariables.Thissectionpresentsbasicdefinitionsandresults.Convergenceinprobability:Asequenceofvariables{xN:N=1,2,…}

12、convergesinprobabil

當前文檔最多預覽五頁,下載文檔查看全文

此文檔下載收益歸作者所有

當前文檔最多預覽五頁,下載文檔查看全文
溫馨提示:
1. 部分包含數(shù)學公式或PPT動畫的文件,查看預覽時可能會顯示錯亂或異常,文件下載后無此問題,請放心下載。
2. 本文檔由用戶上傳,版權(quán)歸屬用戶,天天文庫負責整理代發(fā)布。如果您對本文檔版權(quán)有爭議請及時聯(lián)系客服。
3. 下載前請仔細閱讀文檔內(nèi)容,確認文檔內(nèi)容符合您的需求后進行下載,若出現(xiàn)內(nèi)容與標題不符可向本站投訴處理。
4. 下載文檔時可能由于網(wǎng)絡波動等原因無法下載或下載錯誤,付費完成后未能成功下載的用戶請聯(lián)系客服處理。