22585.非參數(shù)回歸模型方差變點(diǎn)的估計(jì)

1、論文題目：非參數(shù)回歸模型方差變點(diǎn)的估計(jì)專(zhuān)業(yè)：應(yīng)用數(shù)學(xué)研究生：劉彥紅劉彥紅（簽名）：指導(dǎo)教師：王雪峰金浩王雪峰金浩（簽名）：摘要目前時(shí)間序列分析中變點(diǎn)問(wèn)題的研究是統(tǒng)計(jì)學(xué)研究里一類(lèi)熱門(mén)問(wèn)題，也一直備受?chē)?guó)內(nèi)外眾多學(xué)者的關(guān)注。以往的變點(diǎn)研究主要集中在均值發(fā)生變化的情況，如今對(duì)方差變點(diǎn)的研究正處在炙熱時(shí)期。本文首先介紹了變點(diǎn)的相關(guān)背景和研究意義，以及非參數(shù)回歸較參數(shù)回歸的優(yōu)勢(shì)。另外在已有的變點(diǎn)理論和方法的基礎(chǔ)上，用非參數(shù)方法對(duì)兩種情形的時(shí)間序列方

2、差變點(diǎn)進(jìn)行了研究。第一種情形是針對(duì)獨(dú)立隨機(jī)變量單方差變點(diǎn)的研究：針對(duì)獨(dú)立序列均值變點(diǎn)的研究，局部思想法體現(xiàn)出很好的檢驗(yàn)估計(jì)效果，本文在此基礎(chǔ)上用局部思想法和滑窗法的結(jié)合對(duì)獨(dú)立隨機(jī)變量序列中存在方差變點(diǎn)的問(wèn)題進(jìn)行研究，并給出了變點(diǎn)的檢驗(yàn)統(tǒng)計(jì)量和變點(diǎn)的估計(jì)，以及檢驗(yàn)統(tǒng)計(jì)量的極限分布，理論證明了此情形下方差變點(diǎn)估計(jì)的強(qiáng)相合性和強(qiáng)收斂速度，并用實(shí)驗(yàn)數(shù)值模擬驗(yàn)證了此方法的有效性。第二種情形是針對(duì)隨機(jī)設(shè)計(jì)下非參數(shù)回歸模型方差變點(diǎn)的研究：利用局部線(xiàn)性

3、核估計(jì)來(lái)擬合回歸曲線(xiàn)，并構(gòu)造殘差序列及CUSUM檢驗(yàn)統(tǒng)計(jì)量，在一定假設(shè)條件下推導(dǎo)證明了檢驗(yàn)統(tǒng)計(jì)量的漸近分布，驗(yàn)證了檢驗(yàn)統(tǒng)計(jì)量收斂于Brown橋的上確界，并利用不同的核函數(shù)估計(jì)驗(yàn)證了局部線(xiàn)性核估計(jì)對(duì)核函數(shù)的選取影響不大，最后用實(shí)驗(yàn)數(shù)值模擬驗(yàn)證了局部線(xiàn)性核估計(jì)較其他核估計(jì)存在邊界效應(yīng)的問(wèn)題明顯減弱，這樣既改進(jìn)又拓展了原有的方法。最后對(duì)本文做了總結(jié)，并提出進(jìn)一步需要研究的問(wèn)題。關(guān)鍵詞：方差變點(diǎn)；非參數(shù)回歸；變點(diǎn)估計(jì)；檢驗(yàn)統(tǒng)計(jì)量研究類(lèi)型：理論研

4、究Subject:ThenonparametricregressionmodelofvariancechangingpointestimatesSpecialty:AppliedMathematicsName:LiuYanhongLiuYanhong(Signature)Instruct:WangXuefengJinHaoXuefen(Signature)ABSTRACTThechangepointproblemintimeseries

5、analysisisastatisticalstudyofaclassofpopularresearchdirectionhasattractedmuchattentionofmanyscholarsathomeabroad.Studyonthechangepointbefemainlyfocusonthechangesofthemeanvariancechangepointoftheresearchnowisinthehotperio

6、dthispapermainlyusesnonparametricmethodoftimeseriesvariancechangepointoftwocaseswerestudied.Thispaperfirstintroducesthebackgroundsignificanceoftheresearchonchangepointsnonparametricregressionwithparametricregressionadvan

7、tage.Inadditionbasedonthechangepointofexistingtheiesmethodstheuseofnonparametermethodoftwokindsoftimeseriesvariancechangepointarestudied.Thefirstoneistostudythedifferenceofindependentromvariablestounilaterallychangepoint

8、:accdingtothesequenceofmeanchangepointofindependentthoughtlocallawshowsagoodtesteffectofestimationthispaperbasedontheslidingwindowmethodthecombinationofthevariancechangepointproblemsareasequenceofindependentromvariablesw

9、ithlocalthoughtmethodgivestheteststatisticthechangepointestimationofchangepointthedistributionoflimitteststatisticstheyprovesthatthisdifferenceofchangepointestimatunderthestrongconsistencyconvergenceratetheeffectivenesso

10、fthismethodisverifiedbythenumericalsimulation.Thesecondscenarioisbasedonnonparametricregressionmodelunderromdesignvariancechangepoint:theuseoflocallinearkernelestimationtofittheregressioncurvethestructureoftheresidualseq

11、uencetheCUSUMteststatisticsundercertainassumptionsderivedtheasymptoticdistributionoftheteststatisticisprovedtoverifytheteststatisticconvergestothesupremumoftheBrownbridgetheuseofdifferentkernelfunctionestimationtoverifyt