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1、Bernoulli14(3),2008,725748DOI:10.3150/08-BEJ129SmoothedweightedempiricallikelihoodratioconfidenceintervalsforquantilesJIAN-JIANRENDepartmentofMathematics,UniversityofCentralFlorida,Orlando,Florida32816,USA.E-mail:jren@mail.ucf.eduThusfar,likelihood-basedintervalestimat
2、esforquantileshavenotbeenstudiedintheliteratureonintervalcensoredcase2dataandpartlyintervalcensoreddata,and,inthiscontext,theuseofsmoothinghasnotbeenconsideredforanytypeofcensoreddata.Thisarticleconstructssmoothedweightedempiricallikelihoodratioconfidenceintervals(WELR
3、CI)forquantilesinaunifiedframeworkforvarioustypesofcensoreddata,includingrightcensoreddata,doublycensoreddata,intervalcensoreddataandpartlyintervalcensoreddata.Thefourthorderexpansionoftheweightedempiricallog-likelihoodratioisderivedandthetheoreticalcoverageaccuracyequ
4、ationfortheproposedWELRCIisestablished,whichgenerallyguaranteesatleastfirstorderaccuracy.Inparticular,forrightcensoreddata,weshowthatthecoverageaccuracyisatleastO(n−1/2)andoursimulationstudiesshowthatincomparisonwithempiricallikelihood-basedmethods,thesmoothingusedinWE
5、LRCIgenerallyprovidesashorterconfidenceintervalwithcomparablecoverageaccuracy.Forintervalcensoreddata,itisinterestingtofindthatwithanadjustedraten−1/3,theweightedempiricallog-likelihoodratiohasanasymptoticdistributioncompletelydifferentfromthatobtainedbytheempiricallike
6、lihoodapproachandtheresultingWELRCIperformfavorablyintheavailablecomparisonsimulationstudies.Keywords:bootstrap;doublycensoreddata;empiricallikelihood;intervalcensoreddata;partlyintervalcensoreddata;rightcensoreddata1.IntroductionSinceOwen(1988),theempiricallikelihood
7、methodhasbeendevelopedtoconstructtestsandconfidencesetsbasedonthenonparametriclikelihoodratio;seeOwen(1990,1991,2001),Di-Ciccio,HallandRomano(1991),QinandLawless(1994),Mykland(1995)andZhou(2005),amongothers.Studieshaveshownthattheempiricallog-likelihoodratiousuallyhasa
8、nasymp-toticchi-squareddistributionandthattheempiricallikelihoodratioinferenceisofcomparableaccuracytoalternativemethods.Inp
