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1、SequentialEstimationbyMalayGhosh,NitisMukhopadhyayandPranabK.SenCopyright©1997JohnWiley&Sons,Inc.Chapter14SequentialEstimationoftheSizeofaFinitePopulation14.1INTRODUCTIONInavarietyofbiological,ecological,andenvironmentalinvestigations,theestimationofthetotalsizeofapopulationisofconsiderableimpor
2、tance.Inagriculturaloreconomicsurveys,nomatterwhetheranequalorunequalprobabilitysamplingdesignisadopted,N,thetotalnumberofunitsinthepopulation,isassumedtobeknown,althoughthevaríatevaluesofthecharac-teristicsassociatedwiththeseunitsmaynotbeknownapriori.Forexample,N,thetotalnumberoffarmsinagivenst
3、ateorregion,canbereadilyob-tainedfromtheofficialrecords,whiletheiragriculturalholdingsmayhavetobeestimatedbyacompletecensusormoreeconomicallybyusingproba-bilisticsamplingmethods.Inasomewhatdifferentsetup,forexample,intheestimationofanimalabundanceorextinctionofanendangeredspecies,thetotalheadcou
4、ntisnotknown,anditsestimationisofprimaryimportance.Theproblemmayactuallybemorecomplicatedinpracticeduetoemigra-tionandimmigrationandbirth/deathphenomenathatinducechangesinthetotalsizeovertime.Iftheintervaloftimeduringwhichsuchinvestigationiscarriedoutisrelativelysmall,andtherearenosuddenmigrator
5、yorepidemiceffects,thepopulationmaybetakenasclosed,thatis,stationaryovertheperiod,sosimplestatisticalmethodscanbeadoptedtoestimatethisnumberinaconvenientmanner.Fortheestimationofthesizeofsuchaclosedpopulation,amongtheavail-ablemethods,theonesbasedontheso-calledCapture,Mark,Release,andRecapture(C
6、MRR)techniquehavebeenusedmoreextensivelyinpractice.Indeedtheclassical(two-sample)Petersen(1896)estimatorisalandmarkinthisarena,andramificationsofthisestimator,consideredbyvariousre-searchers,willbereviewedsystematicallyinthenextsection,mostlyina39339414.SEQUENTIALESTIMATIONOFAFINITEPOPULATIONnon
7、sequentialsetup.Inthiscontextasimpleurnmodelisusedtofacilitatethestudyofthestatisticalpropertiesoftheseestimators.Thenotablemul-tisampleextensionsoftheseestimatorsarethenpresentedinSection14.3,whiletheinversesamplingschemesa
