Estimation of Population Mean under Non-Response using Various Imputation Methods for Stratified Population
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1 olumba tatoal Publshg Joual of Advacd omutg (5 Vol. o.. - do:.776/ac.5.8 sach Atcl stmato of Poulato a ud o-sos usg Vaous mutato ods fo tatfd Poulato Paa gh *, At Kuma gh, ad V.K. gh cvd: tmb 5 Acctd: 9 tmb 5 Publshd ol: 7 Octob 5 h auo(s 5. Publshd w o accss at Abstact s a, stmatos of oulato ma hav b oosd usg dfft mutato tchqus such as ma, ato ad otal mod, to dal w oblm of o-sos ud statfd adom samlg schm. Post tatfcato has also b cosdd ad fo cosodg ot stmatos, s ad P s hav b obtad fo dfft o-sos at. Kwods: tatfd adom amlg Pootoal Allocato Post tatfcato Pctag latv ffcc. toducto o-sos (o o-covag s a ht chaactstc of a t of oulato ad, fo, caot b lmatd b a mas, a, ffct mods a to b dvlod fo stmatg oulato aamts w hl of mssg data so obtad. A commo tchqu fo hadlg o-sos s mutato, wh mssg valus a flld to cat a comlt data st at ca b aalsd w tadtoal aalss mods. a mutato, hot dc mutato, gsso mutato, ato mutato a all sgl mutato ss at a sgl valu s mutd fo v mssg valu to oduc a comlt data st. o dal w mssg valus ffctvl Kalto t al (98 ad ad (979 suggstd mutato mods at ma a comlt data st stuctuall comlt ad ts aalss. t al (99 usd fomato o a aula vaabl fo uos of mutato. s a w hav cosdd oblm of o-sos statfd samlg schm. tatfd adom samlg sts a samlg schm at attmts to dvd a oulato to suboulatos such at mmbs of ach suboulato a latvl homogous w sct to vaabl of tst ad latvl htogous fom mmbs of o subgous. h am of statfd adom samlg s to slct a saml such a wa at dtfd subgous o oulato a std saml sam ooto at st oulato. h a som wos do statfd adom samlg ud o-sos. Uadhaa ad gh (999 ad gh t al. (7 hav suggstd class of stmatos sml adom samlg. Kadla ad g ( adotd Uadhaa *osodg -mal: a.bhu.vs@gmal.com Datmt of tatstcs, Baaas Hdu Uvst, Vaaas, Utta Padsh, da Datmt of tatstcs, tal Uvst of aasa, aasa, da
2 Paa gh, At K. gh, ad V.K. gh / Joual of Advacd omutg (5 Vol. o..- ad gh (999 stmato statfd adom samlg. gh t al. (8 suggstd class of stmatos usg ow tasfomato basd o stmatos dvlod b Kadla ad g (. Kadla ad g (5, habb ad Guta (5, 6 ad gh ad Vshwaama (8 hav suggstd w ato stmatos statfd samlg to mov ffcc of stmatos, Kadla ad Koucu (9 hav oosd a gal faml of stmatos, whch uss fomato of two aula vaabls statfd adom samlg to stmat oulato ma of stud vaabl. houdha t al ( hav oosd som faml of stmatos fo oulato ma statfd samlg. h uos of s a s to ( ( Poos som stmatos fo oulato ma usg vaous mutato statgs ud assumto of sc of o-sos statfd oulato ad also ud Post- tatfcato ad to stud ots. oma s ad P s ud dfft o-sos at. s a w assum at o-sos s st stud vaabl ol.. otatos h followg otatos hav b usd: : tud vaabl. : Aula vaabl. : tatum ma of statum,,... fo stud vaabl. : tatum ma of statum,,... fo stud vaabl. : z of oulato. : Poulato z of statum,,.... : z of saml, slctd fom t oulato. : z of saml ta fom statum,,.... : umb of sodts, saml slctd fom : Obsvato o,,...,,.... ut statum o stud vaabl : a of sodt gou saml slctd fom vaabl statum,,.... statum,,... of stud : a of sodt gou saml slctd fom statum,,.... Of aula vaabl : Poulato a qua of statum
3 Z Paa gh, At K. gh, ad V.K. gh / Joual of Advacd omutg (5 Vol. o..- : offct of vaato of vaabl Z statum wh Z = (,. Poosd amlg tatgs ad stmato Pocdus t us cosd a oulato cosstg of uts dvdd to stata. t sz of statum s,,,... such at. W dcd to slct a saml of sz fom t oulato such a wa at statum. hus, w hav. Fo uts a slctd fom uts statum, fomato has b obsvd ol o uts, hc to uobsvd ( uts, valus a gv usg obsvd (sodg valus ad/o aula fomato ough vaous mutato tchqus. ag aml aomato: od to fom mamatcal oatos o suggstd stmatos fo fdg Bas ad, w shall us followg lag saml aomatos: wh ( ( ( (,q stads fo q ( ( ( ( (. Poosd mutato tatgs. a mod of mutato ( ( ( ( ( Ud s mod, stud vaat aft mutatos tas fom,. f f ( wh ad sctvl dot sos gou ad o-sos gou ach statum. h ot stmato fo statum s gv b
4 Paa gh, At K. gh, ad V.K. gh / Joual of Advacd omutg (5 Vol. o..- 5 (... ( Hc saml ma fo statum wll b sodt ma of at statum ud s mod. ombg s fo ovall stata, w hav ot stmato of oulato ma as ( ow, sc ( Hc s a ubasd stmat of oulato ma. h vaac of stmat ca b obtad as V V V, (5. ato mod of mutato s mod, w hav cosdd aat t ato stmat whch w ta ato stmat of ach statum ad add s totals. Usg ato mod of mutato fo mssg valus fo statum ˆ f b f. (6 wh b ˆ hc ot stmato fo statum s gv b b b b.. ˆ ˆ ˆ (7 hs s ato stmat fo statum. ombg s fo ovall stata ot stmato of oulato ma wll b:
5 Paa gh, At K. gh, ad V.K. gh / Joual of Advacd omutg (5 Vol. o..- 6 (8 lal s ot a ubasd stmat of oulato ma. o ts Bas B ad ca b obtad as B adg ad tag tms uto od O, w hav B (9 mlal w hav as w hav, tms utood O sso ad tag adg ow
6 Paa gh, At K. gh, ad V.K. gh / Joual of Advacd omutg (5 Vol. o..- 7 (. otal mod of mutato otvatd b Bahl ad uta (99 mutato tchqus utlzg otal-t stmato a dfd as: f f ad f f.. ( ad wh bg uow costat,,... h cosodg ot stmato fo statum ud abov two schms a obtad as ad ( ( Hc combg mutato mods as suggstd abov, ov all stata fo two schms ad usg lag saml aomato, otal-t stmatos fo oulato ma, cosodg bas ad ma squa os a obtad as: ( (
7 Paa gh, At K. gh, ad V.K. gh / Joual of Advacd omutg (5 Vol. o..- 8 B Aft smlfcato of tms ad usg lag saml aomatos, fall B 8 ( Whch wh solvd ud lag saml aomatos, ducd to,,, ( ma : h mmum of occus wh fo whch duc to: (,, (5 ow fo mutato schm, w hav ot stmato fo oulato ma as ( (6 Followg ls of dvatos as dscbd abov fo stmato, bas ad of o otal stmato a obtad as
8 Paa gh, At K. gh, ad V.K. gh / Joual of Advacd omutg (5 Vol. o..- 9, B 8 (7, (8 h mmum of occus wh fo whch ducs to (, (9 5. Us of Post tatfcato fo uggstg Poosd tatgs gal, t s ot alwas ossbl to hav owldg of stata szs as wll as avalablt of a fam fo samlg ach statum. h saml ma b cosdd as ost statfd to two gous ad stg sodg ad o-sodg uts sctvl. uhatm ( advocatd at fo lag saml sz ost statfcato gvs sults as cs as statfd samlg ud ootoal allocato. Hc, w assumd h.. o. of uts as a adom vaabl, so. f so at f ad f wh f f f f ( ag aml aomatos: W cosd followg aomatos: ( ( ( ( ( ( ( ( ( ( ( ( ( ( Ud s codto abov stmatos wll hav followg Bas ad : 5. a mod of mutato: B (
9 Paa gh, At K. gh, ad V.K. gh / Joual of Advacd omutg (5 Vol. o..- V ( 5. ato mod of mutato B ( ( 5. otal mod of mutato:, ( B 8 (5,, (6 h mmum of occus wh fo whch ducs to, (7 B ( 8 (8 (9 h mmum of occus wh fo whch ducs to ( ( 6. mcal tud o llustat fomacs of vaous mutato mods cosdd abov, w hav ta data std Kadla ad g ( wh al oducto amout s ta as stud vaabl ad umb of al ts as aula vaabl 85 vllags of u 999 (ouc: sttut of tatstcs, ublc of u.
10 Paa gh, At K. gh, ad V.K. gh / Joual of Advacd omutg (5 Vol. o..- abl 6. tata as ad a-squa os ( ud tud ad Aula Vaabls, tata o. tata z a a W hav comutd s of vaous stmatos oosd a o bass of s st of data b cosdg two o-sos ats vz 5% ad 5%. h valus of 's ad P s hav b std abl 6.. abl 6. ad P s comaso o-sos ats 5% 5% stmatos tatfcato 6. ( ( ( ( ( ( ( ( s (P s Ud Post tatfcato ( ( ( ( ( ( ( ( ocluso Fom mcal stud, t ca b cocludd at otal mutato mod s mo ffct a ma ad ato mods of mutato ud statfd adom samlg schm ad stmatos a lss ffct ud Post statfcato of saml. hus suggstd otal t stmatos a alwas fabl ov o ts of mutato tchqus. Fu t s vdt at as o-sos at cass oulato all stmatos td to b lss ffct.
11 fcs Paa gh, At K. gh, ad V.K. gh / Joual of Advacd omutg (5 Vol. o..- Bahl,. ad uta,. K. (99: ato ad oduct t- otal stmato, fomato Otmzato sccs,,, haudha,.k, gh., Kuma., hula.k. ad maadach F. (: A lass of aat- stmatos Fo Poulato a tatfd amlg Usg Kow Paamts Ud o sos. ultsac & ultstuctu utosohc asdsclat. ctfc Publcatos. Hao, Flad. haudha,.k, gh V.K., ad hula.k.,(: ombd-t faml of stmatos of oulato ma statfd adom samlg ud o-sos Joual of lablt ad tatstcal tuds Vol. 5, ssu (: -. Has,. H., ad Huwtz, W.. (96: h oblm of o-sos saml suvs. Joual of Amca tatstcal Assocato,, htt://d.do.og/.8/ Kadla,., ad g, H. (5: A w stmato statfd adom samlg. ommucato tatstcs ho ad ods,, htt://d.do.og/.8/a-556 Kadla,., ad g, H. (: ato stmato statfd samlg. Bomtcal Joual, 5, 8-5. htt://d.do.og/./bm.97 Kalto,G.,Kasz,D.ad atos,.(98: ssus of o-sos ad mutato uv of com ad Pogamm Patcato, ut ocs uv amlg(d. Kws,. Plat ad J..K.ao, Acadmc Pss, w o, 55-8 htt://d.do.og/.6/b Koucu,. ad Kadla,. (8: ato ad oduct stmatos statfd adom samlg, Joual of tatstcal Plag ad fc, 9, 8, htt://d.do.og/.6/.s.8..9 Koucu,., ad Kadla,. (9 : Faml of stmatos of oulato ma usg two aula vaabls statfd adom samlg, ommucato tatstcs ho ad ods, 8:, htt://d.do.og/.8/698567, H., acout,. ad adal,.. (99: mts w vaac stmato fom suv data w mutd valus, Joual of Offcal tatstcs, (, -.,H., acout,. ad adal,.. (995: Vaac stmato sc of mutd data fo galsd stmato sstm, Pocdgs of Amca tatstcal Assocato, ocal uv sach ods cto, ad,.g. (979: A soal vw of hot dc mutato ocdus, uv odolog, 5, 8-6. gh,., Kuma,., gh,. D., ad haudha,.k. (8: otal ato stmatos tatfd adom amlg. Pstd tatoal mosum o Otmsato ad tatstcs (..O. at A..U., Algah, da, dug 9- Dc 8. gh,. ad Do, B. (: mutg w ow tasfomato. tatstcal Pas,, htt://d.do.og/.7/bf96 uhatm P.V., ad uhatm B.V.(: amlg o of suvs w alcatos, Push ublcato, w Dlh. hau.., adav K., ad Paa. (: stmato of a w mutato of ssg Data tatfd adom amlg. sach & vws: Joual of tatstcs. Volum, ssu, : 78 7.
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