A New Estimator Using Auxiliary Information in Stratified Adaptive Cluster Sampling
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1 Ope Jourl of ttitic, 03, 3, 78-8 ttp://d.doi.org/0.436/oj Publied Olie eptember 03 (ttp:// New Etimtor Uig uilir Iformtio i trtified dptive Cluter mplig Nippor Cutim *, Moc Cigprdit, ujitt urpee Deprtmet of Mtemtic, Fcult of ciece, Mrkm Uiverit, M rkm, Tild Emil: * j38304@otmil.com Received Jue, 03; revied Jul, 03; ccepted Jul 9, 03 Coprigt 03 Nippor Cutim et l. Ti i ope cce rticle ditributed uder te Cretive Commo ttributio icee, wic permit uretricted ue, ditributio, d reproductio i medium, provided te origil work i properl cited. BTRCT I ti pper, we tud te etimtor of te popultio me i trtified dptive cluter mplig b uig te iformtio of te uilir vrible. imultio owed tt if te vrible of iteret () d te uilir vrible (,) ve ig poitive correltio te te etimte of te me qure error of te rtio etimtor i le t te etimte of te me qure error of te product etimtor. Te etimtor wic ue ol oe uilir vrible were better t te etimtor wic ue two uilir vrible. Keword: trtified dptive Cluter mplig; uilir Vrible; Rtio Etimtor; Product Etimtor. Itroductio dptive cluter mplig, propoed b Tompo [], i efficiet metod for mplig rre d idde clutered popultio. I dptive cluter mplig, iitil mple of uit i elected b imple rdom mplig. If te vlue of te vrible of iteret from mpled uit tifie pre-pecified coditio C, tt i i, i c, te te uit eigborood will lo be dded to te mple. If oter uit tt re dptivel dded lo tif te coditio C, te teir eigborood re lo dded to te mple. Ti proce i cotiued util o more uit tt tif te coditio re foud. Te et of ll uit elected d ll eigborig uit tt tif te coditio i clled etwork. Te dptive mple uit, wic do ot tif te coditio re clled edge uit. etwork d it ocited edge uit re clled cluter. If uit i elected i te iitil mple d doe ot tif te coditio C, te tere i ol oe uit i te etwork. eigborood mut be defied uc tt if uit i i i te eigborood of uit j te uit j i i te eigborood of uit i. I ti pper, eigborood of uit i defied te four ptill djcet uit, tt i to te left, rigt, top d bottom of tt uit ow i Figure. Figure illutrte te emple of etwork. Te uit wit tr i te iitil uit elected. Te coditio to dptivel dded uit i vlue greter t or equl to. * Correpodig utor. Uit tt re to te left, rigt, top, d bottom of oe oter mkig up eigborood. Te uit i te gr dig form igle etwork. Te uit i bold umber re edge uit of te etwork. Te etwork d it edge uit mke up cluter. dptive cluter mplig re pplied i trtified rdom mplig. I dptive cluter mplig, iitil trtified mple i elected from popultio, d weever te vrible of iteret for uit i oberved to tif te coditio, te eigborood of tt uit i dded i te mple. ometime oter vrible re relted to te vrible of iteret. We c obti dditiol iformtio for etimtig te popultio me. Te ue of uilir vrible i commo metod to improve te preciio of etimte of popultio me. I ti pper, we will tud te etimtor of popultio me i trtified dptive cluter mplig uig uilir * Figure. Te emple of etwork were uit eigborood i defied four ptill djcet uit. Coprigt 03 cire.
2 N. CHUTIMN ET. 79 vrible. ome comprio re mde uig imultio.. trtified dptive Cluter mplig For trtified dptive cluter mplig, te popultio coit of N uit prtitioed ito trt bed o prior iformtio bout uit tt re imilr, d it i umed tt te popultio igore croover betwee trt. Te popultio i ec trtum coit of N uit,,,. Te popultio me of te vrible of iteret i trtum i. iitil mple of uit ie i elected b imple rdom mplig witout replcemet d for toe uit elected tt tif te coditio. Te te uit eigborood i dded to te mple. Defie wi j m i j i i te verge of te -vlue of te etwork to wic u belog. i i i te etwork tt iclude uit i i trtum d mi i te ie of etwork tt iclude uit i i trtum. Te etimtor of te popultio me bed o He-Hurwit etimtor (Tompo d eber []) i N t_ w () were Te vrice of were d w i t_ w i w V t _ N N () N N w i N N Te etimte of t_ were w w N. i V i w V t _ N N (3) N w i w w. 3. Propoe Etimtor Te etimtor of te popultio me i trtified dptive cluter mplig uig two uilir vrible (,) i (Wlid. bu-de, M.. med, R.. med d He. Muttlk, [3]), t t _ t _ t _ α = 0 d α = 0 i clled me per uit, α = d i clled multivrite rtio etimtor, d i clled multivrite rtio etimtor, α = d i clled multivrite product etimtor, d 0 i clled rtio etimtor uig, 0 d i clled rtio etimtor uig, d 0 i clled product etimtor uig d 0 d i clled product etimtor uig. et d o Tu t_ e0, e e t_ t_ 0 0 E e E e E e E e V e E e V t _ V t_ Ee NN, E e E e w 0 N N w, NN, N N w w, Ee0e N N w, w Ee0e N N w, w (4) Coprigt 03 cire.
3 80 N. CHUTIMN ET. d Eee N N. o, w, w t 0 e e e e e e e e e e ee e e ME t E t E e e e e e 0 0 ee 0 ee To fid d wic miimie ME t tke prtil derivtive of t ME wit repect to, d et it equl to ero. d d ME t ME t 0 0 o te optimum vlue of d re Te etimte of i d te etimte of i were d w N N, w NN, w, w N N, N N w, w w, w. N N 4. imultio tud Ti ectio, te imultio -vlue -vlue d -vlue from Cutim, N. d Kumpo, B. [4] were tudied. Te dt prtitio ito 4 trtum. Te trtum ie i 0 5 = 00 uit. Te popultio were ow i Figure -4. mple of uit i elected b imple rdom mplig witout replcemet. Te -vlue re obtied for keepig te mple etwork. I ec te mple etwork, te -vlue d -vlue re obtied. Te coditio for dded uit i te mple i defied b C : 0. For ec etimtor 5000 itertio were performed to obti ccurc etimte. Iitil R ie were vried = 5, 0, 5, 0 d 30 were ued. Te etimted me qure error of te etimte me i ME i, i were i i te vlue for te relevt etimtor for mple i. Te etimte of te me qure of te etimtor ME re ow i Tble, were 0 d 0 i clled ME of me per uit, d i clled ME of multivrite rtio etimtor, d i clled ME of multivrite rtio etimtor, d i clled ME of multivrite product etimtor, d 0 i clled ME of rtio etimtor uig, 0 d i clled ME of rtio etimtor uig, d 0 i clled ME of product etimtor uig d 0 d i clled ME of product etimtor uig. 5. Cocluio trtified dptive cluter mplig i efficiet metod for mplig rre d idde clutered popultio. Te umericl tud owe d tt if te vrible of i- Coprigt 03 cire.
4 N. CHUTIMN ET. 8 trtum trtum trtum 3 trtum Figure. Y vlue. trtum trtum trtum 3 trtum Figure 3. X vlue. Coprigt 03 cire.
5 8 N. CHUTIMN ET. trtum trtum trtum 3 trtum ME 00 Figure 4. Z vlue. Tble. Te etimte me qure error of te etimtor. ME 0 0 ME ME ME 0 0 ME ME ME * * teret d te uilir vrible, ve ig poitive correltio te te etimte of te me qure error of te rtio etimtor i le t te etimte of te me qure error of te product etimtor. Te etimtor wic ue ol oe uilir vrible were better t te etimtor wic ue two uilir vrible. 6. ckowledgemet Ti reerc w upported b Fcult of ciece Mrkm Uiverit, Tild. We would lo like to profoudl tk Mr. Pvee Cutim for i progrmmig dvice. of te meric ttiticl ocitio, Vol. 85, No. 4, 990, pp doi:0.080/ []. K. Tompo d G.. F. eber, dptive mplig, Wile, New York, 996. [3] W.. bu-de, M.. med, R.. med d H.. Muttlk, ome Etimtor of Fiite Popultio Me Uig uilir Iformtio, pplied Mtemtic d Computtio, Vol. 39, No. -3, 003, pp doi:0.06/ (0) [4] N. Cutim d B. Kumpo, Rtio Etimtor Uig Two uilir Vrible for dptive Cluter mplig, Jourl of te Ti ttiticl ocitio, Vol. 6, No., 008, pp REFERENCE []. K. Tompo, dptive Cluter mplig, Jourl Coprigt 03 cire.
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