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1、ConvergenceRatesOfNearestNeighborDensityEstimatorsunderNASampleGrade：2013Major：ProbabilityandStatisticsResearchfie]d：StatisticsGraduate：ZhuTiantianSupervisor：QinYongsongABSTRACTTheconceptofnegativelyassociated(NA)sequenc

2、ewasproposedfirstlybyJoag—DeyandProschan(1983)andBlockandSavits(1982)Joag—DeyandProschandiscussedsomebasicprop—ertiesandpracticalapplicationsofNAsequencesRoussas(1994)andBeak(2003)alsostudiedthebasicpropertiesofNAsequenc

3、essuchascompleteconvergenceDuetothebroadapplicationsofNAsequences，thestatisticalinferencesassociatedwithNAsequenceshaveattractedgreatatten—tionsofmanyscholarsLargesamplepropertiesofNAsequencessuchastheasymptoticnormality

4、ofkerneldensityestimationhavebeeninvestigatedextensivelyNearestneighbordensityestimatorisanimportantnon—parametricdensityestimationmethod，whichwasproposedbyLoflsgardenandQuesenberryin1965Theyprovedtheweakconsistencyofnea

5、restneighbordensityestimator厶(z)Sincetheconceptofnearestneighbordensityesti—matorwasintroduced，manyscholarsstudieditscharacteristicssuchasconsistencyanduniformconvergenceunderallkindsofsamplesandvariousconditionsAsaresul

6、t，alotofgoodresultshavebeenobtainedinthisaspectAccordingtotheideaofnearestneighborestimator，Yuproposedanewnearestneighbordensityestimator厶(z)basedonorderstatisticsin1986Underindependentsamplesandmildconditions，heestablis

7、heditspointwiseweakandstrongconsistencyuniformweakandstrongconsistencyandtheL1一moldstrongconsistencyonaboundedintervalXue(1992，1994)con—sideredtheconsistencyandconvergenceratesof厶(z)underindependentand妒一mixingsamplesresp

8、ectivelyThispapermainlystudiesthepointwiseconsistencyandstronguniformconsistencyandobtaintheconvergenceratesofpointwiseconsistencyanduniformstrongconsistencyofin(z)respectivelyHerewesummarythemainlynewfindingsandinnovati

9、onsinthispaper：1Thispaperfirstlyprovestheconsistencyofnearestneighbordensityestimator厶(z)andobtainstheconvergenceratesunderNAsample2Themethodfromthispapercanprovideagoodreferenceforstudyinglargesamplechar—acteristicsof厶(

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