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1、SequentialEstimationbyMalayGhosh,NitisMukhopadhyayandPranabK.SenCopyright©1997JohnWiley&Sons,Inc.Chapter10NonparametricSequentialConfidenceEstimation10.1INTRODUCTIONThebasicproblemoffindingasequentialconfidenceset,havingaprescribedcoverageprobabilityorconfidencecoefficientandanupperboundforitswidt
2、h,wastreatedinaparametricframeworkinChapter8.Inthatchapterthefocuswasprimarilyonnormaldistributionalmodelsinunivariateandmultivariatesetups.InChapter9,indealingwiththe(asymptotic)mini-mumrisk(point)estimationproblem,ageneralclassofestimatorsinnon-parametricaswellassemiparametricsetupswereconsidere
3、d.Thesequentialconfidencesetestimationproblemsforthesemodelswillbepresentedhereinasystematicandunifiedmanner.Intheliteraturesuchconfidenceintervals(andsets)aregenerallytermedfixed-widthorbounded-lengthintervals(andbounded-diametersets).Inthenonparametriccase,generally,thebounded-widthorbounded-dia
4、meterconfidencesetsaremorepopular,andhence,wewilladoptthatterminologyhere.FurtherinChapter9weobservedthatsomeofthenonparametricestimators((/-statisticsand¿-estimators)areformu-latedalongthelinesofthesamplemean,albeitintheframeworkofamoregeneral"estimableparameter,"whiletheothersarebasedonsuitable"
5、esti-matingequations"andtherebyrelyonappropriatealignmentstatistics.Thesamecharacterizationholdsfortheconfidencesetestimatorstobeconsideredinthischapter.Wepresentthegeneraltheoryofsequentialconfidencesetsinthenonparametriccaseundertwobroadcategories:Type-Aproceduresarebasedonappropriatepointestima
6、torsandtheirdistributions,whileType-Bproceduresmakeuseofthealignmentschemetoagreaterextent.TheseproceduresarepresentedinSections10.2and10.3,respectively.Section10.4dealswiththemultiparametercase.InviewofthebasicdevelopmentsinChapter9,throughoutthischapter,repeatedreferenceswillbemadetotheappropria
7、teresultsinChapter9,andofteninthisprocesstheirderivationsarerelegatedasexercises.Moreoverasymptoticconsiderationsplayavitalrole31531610.NONPARAMETRICSEQUENTIALCONFIDENCEESTIMATIONinthiscontext,andonlyinsomesimple
