數(shù)據深度和基于數(shù)據深度的多維中位數(shù)的穩(wěn)健性分析.pdf

1、浙江大學理學院碩士學位論文數(shù)據深度和基于數(shù)據深度的多維中位數(shù)的穩(wěn)健性分析姓名：羅燕申請學位級別：碩士專業(yè)：概率論與數(shù)理統(tǒng)計指導教師：林正炎20090428AbstractTheorderstatisticsofonedimensiondistributionhasaverywiderangeofapplicationHoweveritdoesnothingforthedataswhichcomefromthemultivariatedi

2、stributionWiththedevelopmentofstatistics，datadepthcomesintobeingwhichservicingforthefamilyofmultivariatedistributionItisappliedfrequentlyforthemultivariatelocationestimate，nonparametrictestandSOonTherobustnessanalysisfor

3、astatisticalfunctionisoneofthemostimportantworksRobustnessanalysisforsomedatadepthsandthemultivariatemediansisthemainaimofthisarticleInfluencefunctionandbreakdownpointaretwepresentationalconceptionsofrobustnessanalysisHe

4、ncethisarticlewillanalyzetheinfluencefunctionandthesamplebreakdownpointofsomedatadepthsandthemultivariatemedianwhichisdefinedbasedonthedatadepthAftersomebriefintroductionforthenotionofdatadepthanditsproperties，wewillanal

5、yzethedatadepthbasedonthespatialrankwhichwasconstructedin【3】Wetake萬(x，F(xiàn))asthiskinddatadepthWiththeanalysiswewillgetthelocalrobustnessoff(x，F(xiàn))AndtheasymptoticofthesampleinfluencefunctionofD(x，F(xiàn))Anotherworkofthisarticleisa

6、nalysisofthebreakdownpointofmultivariatemedianbasedonethe上2datadepth(￡2D(工，F(xiàn)))AndSOisthemedianbasedontheweightedL2一datadepth(形三2D(x，F(xiàn)))SamplebreakdownpointofastatisticalfunctionhastwotypesOneistheadditionsamplebreakdownp

7、oint，andanotheristhereplacementsamplebreakdownpoint【4】hadanalyzedthesimplifiedreplacementsamplebreakdownpointofthemultivariatemedianbasedonwL2D(X，F(xiàn))，Thisarticlewillanalyzeboththeadditionandsimplereplacementsamplebreakdow

8、npointsofthemultivariatemedianbasedonL2D(x，F(xiàn))WealsoanalyzethemedianbasedonWL2D(x，F(xiàn))whoseweightedfunctionhassomedifferentfittedconditionsAndgettheirglobalrobIlstnessintheendKeywords：Datadepth；Robustness；Samplebreakdownpoi