12701.正相協(xié)樣本下最近鄰密度估計的收斂速度

1、正相協(xié)樣本下最近鄰密度估計的收斂速度專業(yè)名稱：概率論菊數(shù)理統(tǒng)計申請A：盧林摹指導(dǎo)老師：秦永松教授論文答辯委員會主席：委員：攀ConvergenceRatesofNearestNeighborDensityEstimatorunderPASamplesGrade：2013Major：ProbabilityandStatisticsResearchfield：StatisticsGraduate：LuLinShenSupervisor：Qi

2、nYongsongABSTRACTTheconceptofpositiveassociatedrandomvariableswasfirstproposedandresearchedbyEsaryProschanandWa／kupin1967ThisconcepthasbeenwidelyusedinstatisticaImechatlic一8，penetrationtheoryreliabilityanalysisandotherfi

3、eldsTherearemanyscholarsmakingdeepstudyonPAItiseasytoseethattherelatedpropertiesandmomentinequalitiesofPArandomvariableshavebeendiscussedintheliterature[1一】9]thenearestneighbordensityestimationmethodinengineeringandtechn

4、ical，physicalsciences，etcLoftsgardenandQuesenberryfirstintroduced1965ItiswidelyusedintheSocialSciences，Atpresent，therearemanyresearchesaboutthenearestneighbordensityestimationFromtheliterature[2343]，wecanseet11atmeconsis

5、—tencYandconvergencerateundertheindependentsamplesandthedependentsamples(includingnegativeassociation，dmixed，etc)havebeenstudiedextensivelyInthispaperwestudytheconsistencyandconvergenceratesofthenearestnei曲bordensityesti

6、mationunderthePAsamplesItisprovedthatthestrongcoIⅣergencerateofthenearestneighbordensityestimatoriscloseton一1／h，andtheuniformlystrongconvergencerateisalmostn上／oforthePAsamplesWefurtherstudytheuniformstrongconsistencyofth

7、eestimationofthefailureratefunctionunderthePAsamplesAttheSalTletime，thenearestneighbordensitvestimation1Smadebynumericalsimulation，andtheadvantagesanddisadvantagesofthenearestneighbordensityestimationmethodarecomparedSom

8、enewfindingsofthispaperaresummarizedasfollows：【1)InthispaperwefirststudytheconsistencyandconvergencerateofthenearestneighbordensityestimatorunderthePAsamples【2)Inthispaper，weprovethatthestrongconvergencerateandtheunifbrm

9、strongcorlVergencerateofthenearestneighbordensityestimationunderthePAsamplesisconsistentwiththatofthenegativeassociatied(NA)samplesKeywords：PASamples；NearestNeighb。rEstimatorofDensityFunction；StrongConsistency；StrongUnif