20754.～ψ混合序列的強(qiáng)收斂性及在半?yún)?shù)模型中的應(yīng)用

1、獨(dú)創(chuàng)性聲明本人聲明所呈交的學(xué)位論文是本人征導(dǎo)師指導(dǎo)F進(jìn)行的研冗工作及取得的研究成果。據(jù)我所知，除了文中特別加以標(biāo)注和致謝的地方外，論文中不包含其他人已經(jīng)發(fā)表或撰寫過的研究成果，也不包含為獲得理㈣或其他教育機(jī)構(gòu)的學(xué)位或證書而使用過的材料。與我一同工作的同恚對本旃究所做的任何貢獻(xiàn)均已在論文中作了明確的說明并表示謝意。學(xué)位敝儲簽名：葛博梅簽字日期：哪引月歲日學(xué)位論文版權(quán)使用授權(quán)書本學(xué)位論文作者完全了解墳篇蚓嗨有關(guān)保留、使用學(xué)位論文的規(guī)定，有權(quán)

2、保留并向國家有關(guān)部門或機(jī)構(gòu)送交論文的復(fù)印件和磁盤，允許論文被查閱和借閱。本人授捌酣可以將學(xué)位論文的全部或部分內(nèi)容編入有關(guān)數(shù)據(jù)庫進(jìn)行檢索，可以采用影印、縮印或掃描等復(fù)制手段保存、匯編學(xué)位論文。(保密的學(xué)位論文在解密后適用本授權(quán)書)學(xué)位論文作者簽名：雞梅梅簽字日期：勘f歲年e月戶日學(xué)位論文作者畢業(yè)去向：工作單位：通訊地址：導(dǎo)師簽名：彥鏘簽字日期：矽玎年多月5日電話：郵編：英文摘要AbstractWehavestudiedtheprobabi

3、litylimittheoryofindependentrandomvariablesButinmanypracticalproblems，thesamplesoftenarenotindependentThelimittheoryofdependentsequencesisoneofthecentralissuesforstudy—ingprobabilitywhichhasverywideapplicationinfieldssuc

4、hasreliabilitypenetrationtheorymultivariatestatisticalanalysis，riskassessment，weatherforecast，stocksandbondsInthisarticle，weinvestigatestrongconvergencepropertiesforweightedsumsof弘mixingrandomvariablesbyseveraltech—nique

5、ssuchasGinequalityMarkov’SinequalityJensen’Sinequalitymomentinequalityrandomcontrolforrandomvariables，etc，andobtainsituationofsemiparametricregressionmodelbasedon≯mixingerrorsInchapter1，firstofall，theauthorintroducetheba

6、ckgroundandcurrentstudiedresultsecondly，someusedinequalitiesaregivenfinally，thestructureofthearticleisgivenInchapter2，thestrongconvergenceforweightedSUIllSof乒mixingse—quenceisstudiedbyusingthemomentofinequalitiesandtheco

7、nditionofrandomcontrolfor乒mixingrandomvariables，andsomesufficientconditionstoprovethestrongconvergenceforweightedsumsof≯mixingsequencearegivenTheresultsextendsomecorrespondingonesforindependentsequencesInchapter3，westudy

8、parametriccomponentandnonparametricCOnlponentestimatorsinasemiparametricregressionmodelbasedon蘆mixingrandomvariables；theirr—thmeanconsistencycompleteconsistencyanduni—formconsistencyareobtainedundersuitableconditionsTher

9、esultsimprovetheconditionsintheliteratureandgeneralizetheexistingresultsofindepen—dentrandomerrorstothecaseof豇mixingrandomerrorsKeyWords：≯mixingrandomvariables；weighedsums；strongconver—gence；fixeddesign；semiparametricreg