25582.相協(xié)樣本下密度函數(shù)在有限個(gè)點(diǎn)處的同時(shí)統(tǒng)計(jì)推斷

1、相協(xié)樣本下密度函數(shù)在有限個(gè)點(diǎn)處的同時(shí)統(tǒng)計(jì)推斷Statisticalinferenceofdensityfunctionsatanumberofn●J●■■nnltepoIntsUnderassociatedsamples作者：朱海江Author：ZhuHaijiang_。__●●___●●_●●_____●______________________________________________；___一指導(dǎo)教師：秦永松專業(yè)：應(yīng)用數(shù)學(xué)

2、學(xué)Supervisor：Qi翌!魚墜g曼Q望gMajor：AppliedMathematics一●_____________________________●_____●_______________________________________________________________________________________________________一Degree：墜堡!塑主里!魚￡曼堡i里里堡里授予單位：塹鎏塹

3、整盔堂Institute：圣墜gi塑g盟Q!坐型墮墜i翌!曼絲YMay2014AbstractIn1967Esaryeta1【1】introducedtheconceptofpositivelyassociatedrandomvari—ables(rVs)intothestatisticalliteratureNegativeassociationofrvswasintroducedbyJoagDevandProschan[21in19

4、83BothpositivelyassociatedsamplesandnegativelyassociatedsamplesarecalledassociatedsamplesIthasbeendiscussedbymanystatisticiansAsthesumsofassociatedrandomvariablessequenceisnotonlywidelyusedinsomereliabilitytheoryproblems

5、，hydromechanics，timeseriesmodels，butalsousedinecologicalsystemandsomeclinicaltrialsThestatisticalinferenceofdensityfunctionsatafinitenumberofdifferentpointsunderassociatedsamplesarestudiedItisshownthatthejointasymptoticd

6、istributionsaremulti—normaldistributionsbyblockwisetechnologyWeextendthemethodinQineta1[3landXiongandLin[4】ofkernelestimationfromasinglepointtomultiplepointsSOastoprovethelogarithmempiricallikelihoodratioofdensityfunctio

7、nsatafinitenumberofdifferentpointsisasymptoticthechisquaredistributionunderassociatedsamples，andthenconstructempiricallikelihoodconfidenceregionsfordensityfunctionsatafinitenumberofdifferentpointsWealsodoasimulationstudy

8、TheresultsshowthatthecoverageprobabilityoftheempiricallikelihoodconfidenceintervalofthedensityfunctionsdifferenceatanytwopointsisquitegoodThenewfindingsinthispapermaybesummarizedasfollows：1Thispaperinvestigatesthejointas

9、ymptoticdistributionsofestimatorsofadensityfunctionatafinitenumberofdifferentpointsunderassociatedsamples，byusingtheblockwisetechnologytoprovethatthejointasymptoticdistributionsaremulti—normaldistributions2Thispaperexten

10、dstheempiricallikelihoodfordensityfunctionfromasinglepointtomultiplepoints，Itisshownthattheasymptoticdistributionofdensityfunctionsatafinitenumberofdifferentpointshaschisquaredistributionunderassociatedsamplesandconstruc