Copyeditedby:AA 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 Journal of Statistical Computation and Simulation Vol.00,No.0,Month2009,1–17 Efficient estimators for adaptive two-stage sequential sampling MohammadSalehi a *,MohammadMoradi a ,JenniferA.Brown b andDavidSmith c a Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, Iran; b Department of Mathematics and Statistics, University of Canterbury, Private Bag 4800, Christchurch, New Zealand; c Leetown Science Center, US Geological Survey, 11649 Leetown Road, Kearneysville,WV 25430, USA Q1 (Received 16 January 2009; final version received 29 April 2009 ) Instratifiedsampling,methodsfortheallocationofeffortamongstratausuallyrelyonsomemeasureof within-stratumvariance.Ifwedonothaveenoughinformationaboutthesevariances,adaptiveallocation canbeused.Inadaptiveallocationdesigns,surveysareconductedintwophases.Informationfromthefirst phaseisusedtoallocatetheremainingunitsamongthestratainthesecondphase.Brown et al. [Adaptive two-stage sequential sampling, Popul. Ecol. 50 (2008), pp. 239–245] introduced an adaptive allocation samplingdesign–wherethefinalsamplesizewasrandom–andanunbiasedestimator.Here,wederive anunbiasedvarianceestimatorforthedesign,andconsiderarelateddesignwherethefinalsamplesizeis fixed.Havingafixedfinalsamplesizecanmakesurvey-planningeasier.WeintroduceabiasedHorvitz– Thompsontypeestimatorandabiasedsamplemeantypeestimatorforthesamplingdesigns.Weconduct twosimulationstudiesonhoneyproducerinKurdistanandsyntheticzirconiumdistributioninaregionon themoon.Resultsshowthattheintroducedestimatorsaremoreefficientthantheavailableestimatorsfor bothvariableandfixedsamplesizedesigns,andtheconventionalunbiasedestimatorofstratifiedsimple random sampling design. In order to evaluate efficiencies of the introduced designs and their estimator furthermore, we first review some well-known adaptive allocation designs and compare their estimator withtheintroducedestimators.Simulationresultsshowthattheintroducedestimatorsaremoreefficient thanavailableestimatorsofthesewell-knownadaptiveallocationdesigns. Keywords: stratifiedpopulation;Neyman’sallocation;Horvitz–Thompsontypeestimator;samplemean typeestimator Q2 AMS Subject Classification: 62D05;92-08 1. Introduction Inconventionalstratifiedsampling,thepopulationispartitionedintoregionsorstrata,andasimple randomsampleisselectedineachstratum,withtheselectionsinonestratumbeingindependent ofselectionsintheothers.Toobtainthebestestimateofthetotalpopulationwithagiventotal Q3 sample size or total survey cost, or to achieve a desired precision with minimum cost, optimal allocation of sample size among the strata is necessary, which results in larger sample sizes in stratathatarelarger,morevariableandlesscostlytosample[1,2]. *Correspondingauthor.Email:salehi-m@cc.iut.ac.ir ISSN0094-9655print/ISSN1563-5163online ©2009Taylor&Francis DOI:10.1080/00949650903005664 http://www.informaworld.com TechsetCompositionLtd,Salisbury GSCS400738.TeX Page#: 17 Printed:15/5/2009