一類平穩(wěn)過程的極限性質(zhì).pdf

1、浙江大學(xué)理學(xué)院博士學(xué)位論文一類平穩(wěn)過程的極限性質(zhì)姓名：劉衛(wèi)東申請學(xué)位級別：博士專業(yè)：概率論與數(shù)理統(tǒng)計指導(dǎo)教師：林正炎20080401AbstractThefirstpartofthispaperconcernssomelimitpropertiesofaclassofstartionaryprocesses(ie溉=9(，％一1，島))，includingstronginvarianceprinciplesforpartialsums，

2、themaximumofperiodogramsandasymptoticsofthespectraldensityestimationThesesunectsareveryimportantinprobabilityandstatistics，andhavebeenexploredinmanyclassicaltextbooksBecauseofasurgeofinterestinnonlineartimeseries，peoplep

3、roposedmanynewquestionsonthesubjectsreferredaboveForexample，canweconsidersimilarproblemsfornonlineartimeseriesItiswellknownthatmartingaleapproximationisaneffectivemethodtodealwithstationaryprocessesHowever，martingaleappr

4、oximationseemsnotverysuitablefortheproblemsaboveForthisreason，weusemdependenceapproximationandobtaintheoptimalratesforstronginvarianceprinciples，theasymptoticdistributionsofthemaximaofperiodogramsofnonlineartimeseriesand

5、themaximumdeviationofthespectraldensityestimationMeanwhile，wesolvesomeopenquestionsproposedbysomepreviouspapersThesecondpartofthispaperconcernsthetestonindependencebetweencomponentsofahighdimensionalvectorThehighdimensio

6、nproblemisverypopularrecentlySincetheindependenceisusuallyassumedinmanystatisticalproblem，testonindependenceisanimportantproblemBasedonsomepreviouswork，weproposeanewstatistictotestwhethercomponentsaleindependent。Wealsopr

7、ovethatthelimitdistributionofthisstatisticistheextremedistributionoftype1witharateofconvergenceO((109n)5／2／何)T虹ismuchfasterthan0(1／logn)，atypicalconvergencerateforthistypeofextremedistributionThethirdpartofthispaperconsi

8、dersLILforindependentBvaluedrandomvariablesBasedonthepreviousliterature，weprovesomeLILforindependentBvaluedrandomvariableswhentheirval瞳ancesareinfiniteSomepreviousresultsaleextendedKeywordsStationaryprocess，stronginvaria