Relationship Pattern of Poverty and Unemployement in Indonesia with Bayesian Spline Approach

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1 Itertol Jourl of Bsc & Appled Sceces IJBAS-IJENS Vol: No: 06 9 Reltoshp Ptter of Poverty d Ueployeet Idoes wth Byes Sple Approch I Nyo Budtr, Rt D, Purhd d 3 Stwko Dresto Lecturer of Sttstc Deprtet, Sepuluh Nopeber Isttute of Techology ITS Cpus, Sukollo, Surby 60 College Studet of Sttstc Deprtet, Sepuluh Nopeber Isttute of Techology ITS Cpus, Sukollo, Surby 60 3 BPS-Sttstcs Idoes Jl. Dr. Sutoo No.6-8, Jkrt 070 Abstrct Poverty s oe of fudetl probles whch becoe jor cocer of Idoes Goveret. World Poverty Cosso sd tht ueployet s oe of the cuses of poverty. A lot of ltertures stte tht there s strog correlto betwee ueployet d poverty, but to prove t eprclly, ws ot esy. To see the reltoshp ptter betwee poverty d ueployet Idoes, t c be used sple opretrc regresso odel. Sple esttor opretrc regresso c be obted by Byess pproch by usg pror Guss proper d order to choose the optl soothg preter, Geerlzed Cross Vldto (GCV) ethod s choose. Reltoshp odel of poverty d ueployet Idoes obted the for of qudrtc sple odel wth two optl kots where percetge of poverty s qudrtc curve d rse the stge whe ope ueployet rte s less th 3.87, d wll be decled whe the ope ueployet rte oved betwee 3.87 d 4.4. But fter the ope ueployet rte reched 4.4, the percetge of poverty re-pttered qudrtclly but decresed slowly. So, for the cse Idoes, udrectol reltoshp betwee poverty d ueployet the rego occurred oly prtlly, whle soe re ctully spg. Key Words: opretrc regresso odel, sple, Byess, GCV. Itroductos Poverty s oe of the fudetl ssues whch becoe jor cocer of Idoes goveret. It s evtble tht oe of poverty cuse s ueployet. Ueployet dctor selecto bsed o the fct tht the dctor s drectly relted to coe levels. World Poverty Cosso lso oted tht ueployet s jor cuse of poverty [33]. Theoretclly, the poverty rte wll ove to follow the rte of ueployet. I ths cse whe the ueployet rte crese the the poverty level wll utotclly crese. Postve reltoshp betwee poverty d ueployet re foud severl coutres. I Kore, for exple, [3] foud very strog reltoshp betwee poverty levels d ueployet rtes. Whe the ueployet rte creses, the poverty rte lso rose d whe the level of ueployet cled, the poverty levels lso fell. However, the chges betwee ueployet level d poverty re ot lwys cosstet s tht foud studes other coutry. For exple, s quoted by [0] bsed o reserch the Uted Sttes foud tht poverty does ot hve strog correlto wth ueployet. Def [0] further stted tht the reltoshp betwee ueployet d poverty s strogly flueced by how poverty s esured. O the other hd, the wek reltoshp betwee poverty d ueployet c lso be cused by wek esureet of the rte of ueployet. Ths s evdeced by the [37] bsed o ther study usg Brzl dt. So d Kkw [37] propose ew esure of ueployet bsed o ot oly the ueployed but lso those whose ergs re below the u wge set by the goveret. By odfyg the covetol ueployet rte esureets they foud tht the correlto betwee ueployet d poverty s very sgfct, whle the sze of ueployet IJBAS-IJENS Deceber 0 IJENS

2 Itertol Jourl of Bsc & Appled Sceces IJBAS-IJENS Vol: No: 06 0 bsed o the covetol reltoshp betwee ueployet d poverty do ot see sgfct. How does the ptter of the reltoshp betwee poverty d ueployet Idoes? A lot of lterture stte tht there s close lk betwee ueployet d poverty, but to prove t eprclly s ot esy. I purpose to odellg the reltoshp betwee poverty d ueployet Idoes, where the ptter of reltoshp s ot kow dvce, the used opretrc regresso odel. Nopretrc regresso odels tht ofte gets the tteto of the reserchers s the Kerel ([38], [5]), Sple ([3], [47], [8], [], [8]), Fourer seres [] d wvelets [3]. Aog the opretrc regresso odel bove, the sple s odel tht hs very specl d very good sttstcl d vsul terpretto becuse t hs hgh flexblty ([], [3]). Besdes, sple s ble to hdle dt chrcter / fucto propertes of sooth d fluctute the subsub-tervl ([6], [3]). It hs lso bee show by [4] whch copres Kerel soothg sple techque wth the dt of gross tol product of Turkey. Sple s polyol fucto for whch s defed sub-sub-tervls (pecewse polyol). Boudry pots of these tervls re clled kots. The kot wll coect the polyols whch re defed o the subtervls such wy to for cotuous fucto. How y kots d where kots re locted re soe of probles sple usg. Aother proble s sple bss fuctos selecto. There re severl bses fuctos of sple, cludg power cuts, cubc sple, d B- sple. Sple esttor c be obted by solvg the pelzed lest squre (PLS) optzto or ze the uber of dt tches (Goodess of ft) d the sze of curve soothess. Sple esttor opretrc regresso developed by y reserchers by tkg the vrto the Goodess of ft d sze of curve soothess. Keldorf d Whb [8], Crve d Whb [8] d Whb [46] produces turl sple esttor (the orgl). Sple esttor s recoeded for beg use o sooth dt. Cox d O Sullv [6] obt the M-type sple esttors to del wth outlers opretrc regresso. Oehlert [30] provde relxg sple esttor d [9] gves the qutle sple esttor. Budtr, et. l [8] gves weghted sple esttor to del wth equlty of vrce (heteroskedstc) opretrc regresso. Sple ts developet, t c ot resolve the proble of ferece such s cofdece tervls for regresso curve. For tht [44] provde Byes pproch for the orgl sple esttor Guss respose dt d [45] lso hve to costruct cofdece tervls for the orgl sple odel. Gu [4] hs developed the results obted by [44] for o-guss respose dt. Sth d Koh [36] usg Byes pproch esttg B- sple fuctos bvrte opretrc regresso odel wth utocorrelto error. Budtr d Subr [9] geerlze the Byes pproch of [45] for weghted sple esttor opretrc regresso. Holes d Mlck [6] usg Byes lyss ultvrte ler sple odel regresso for Guss respose dt. Berry, Crroll, d Ruppert [5] usg Byes pproch to odel the soothg regresso sple fucto d regresso P-sple wth the presece of esureet error. Adebyo [] usg Byes pproch wth B-sple bss fuctos for the odel of lourshed chldre Zb. Crceu, Ruppert d Wd [7] deostrted the use of BUGS sepretrc regresso odels. Chb d Greeberg [4] developed Byes lyss for opretrc regresso odels wth cubc sple bss fuctos d xture of Drchlet processes dstrbuted errors the dt tht [43] regrdg the credt rtg fr Stdrd d Poor's. I ths pper, opretrc regresso odel whch s used odelg the reltoshp betwee poverty d ueployet Idoes s sple odel wth Byes pproch. Pror dstrbutos used ths reserch s lted dstrbuto Guss Iproper pror.. Sple Esttor Gve the odel of opretrc regresso y = f(t ) + ε, t [,b], =,,,. The for of regresso curve s ssued ukow d s coted the Sobolev spce W [, ] b, where W [, ] b = { g ; b ( ) ( g ( t)) dt < }. Rdo error ε s ssued depedet orlly dstrbuted wth zero e d IJBAS-IJENS Deceber 0 IJENS

3 Itertol Jourl of Bsc & Appled Sceces IJBAS-IJENS Vol: No: 06 vrce σ. Sple esttors opretrc regresso re obted by solvg Pelzed Lest Squre (PLS) optzto : M { R(f) + λ J(f) } f W [, b ] Qutztos of R(f) d J(f) stte goodess of ft d esure of the soothess of fucto respectvely. The soothg preter λ cotrols betwee R(f) d J(f). Sple esttors opretrc regresso re developed by y reserchers by vred R(f) d J(f). Whb [47] took R(f) d J(f) qudrtc for : R(f) = ( y j f ( t j )) d j= b ( ) J(f) = [ f ( t)] dt. Accordg to [8], the for of sple esttor ˆf λ s obted by fdg the vlue of f W [, ] b whch zes for : b ( ) ( ( )) + λ ( ( )) = () y f t f t dt Optzto proble equto () c be solved usg Reproducg Kerel Hlbert Spce pproch [8]. Sple optzto c be trsfored to projecto proble o Hlbert spce [38]. The very portt propertes of Reproducg Kerel re we c detere the represetto of fte ler fuctol, such tht regresso curve f W [, b] whch s the optzto soluto of equto () c be foud. If H R = H 0 H d φ,..., φ sp H 0 spce d T s full colu rk trx of order T = Lφ, =,,, gve by { } d v=,,,, the fucto f whch zes ( y f ( t )) + λ P f R s = fˆ λ = α φ + βψ ψ = Pη v v v= =, where α α α = (,..., ) ' = ( T'M T) T' M y β = (,..., ) ' β β v = M (I - T(T'M T) T'M )y M = Σ + λi Σ = < ψ, ψ >,, j =,,3,,. { j } [47] hve show tht the sple esttor tkes for turl sple polyol. 3. Byes Approch for Sple Esttor The selecto of pror dstrbutos Byes pproch s very portt thg. Pror forto used ths reserch s proper Guss pror whch s cobed wth sple forto, usully expressed the lkelhood fucto to fd ts posteror dstrbuto. Byes pproch for pot estto s obted fro posteror e, d tervl estto s obted fro ts posteror vrce. Gve splg observto ( t, y ), ( t, y ),..., ( t, y ), obted fro stochstc process { y( t), t [, b] } the odel y f ( t ) ε, t [, b] { f ( t); t [, b] } dstrbuto, d follows = +, =,,,. hs proper Guss pror / ( ) = αvφv ( ) + β ( ) v= f t t Z t where polyol coeffcet ' α = ( α, α,..., α) ~ N(0, τ I), τ, τ, β s postve costt, d t ( t u) ( ) Z( t) = dw ( u)! s Weer process wth E( Z( t )) = 0 d Reproducg Kerel covrce Cov( Z( s), Z( t)) = { ψ ( s, t)} whch ψ ( s, t) = b ( s u) + ( t u) + [( )! ] du Aother ssupto s polyol coeffcet α v, v =,,..., wth Z( t ) ot correlted [45] d { ε (t)} s Guss process wth E( ε ( t)) = 0, d ( ε ( ), ε ( )) Cov t s σ, f t = s = 0,f t s IJBAS-IJENS Deceber 0 IJENS

4 Itertol Jourl of Bsc & Appled Sceces IJBAS-IJENS Vol: No: 06 If gve Guss rdo vectors y, f, ε wth zero e d follow odel y = f + ε, whch E( f ) = 0, E( ff ') = βσ f, E( ε) = 0, E( εε ') = σ I d E( fε ') = 0, the E( y) = 0 d Vr( y) = βσ f + σ I. If h hs orl dstrbuto wth E( h) = 0, E( hh ') βσ, E( hε ') = 0, d E( hf ') = βσ the hf hf f = h E( h y) = Σ ( Σ + λ I) y d Vr( h y) = β ( Σ Σ Σ Σ ) h hf f fh + σ Σ Σ A(λ) Σ Σ wth hf f f fh A(λ) = Σf ( Σf + λ I ) d Suppose T = { φ t } v λ = σ / β. ( ), =,,, / v=,, the f = Tα + β Z (t). Assued tht α ~ N( 0, τi ) d Z ~ N( 0Σ, ) utully depedet, the / / E( ff ') = E ( + β (t))( + β (t))' Tα Z Tα Z = τ TT' + βσ. Becuse E( ff ') = βσ f the τ Σ = f E( ff ')= TT ' β β + Σ or Σf = ϕττ ' + Σ wth ϕ = τ / β. If we tke h = f ( t), the / / ( hf ) = ( φα + β )( Tα + β Z ) E ' E ' Z(t) (t) ' = τφ ' T' + βψ ' d t / / ( hh ) = ( φ α + β )( φ α + β ) E ' E ' Z(t) ' Ζ(t) ' = τφ ' φ + βψ(t,t). Becuse E( hf ') = βσ hf d ( hh ) = h E ' βσ, the Σhf = E( hf ') = ϕ φ ' T' + ψ t ' d β Σh = E( hh ') = ϕ φ ' φ + ψ( t,t ). β Usg qudrtc loss fucto, we fd tht esttor f λ (t) s the posteror e f, hece by tkg h = f(t), we get fλ, ϕ (t) = E( f(t) y) =Σhf ( Σf + λ I) y = ( φ (t),..., φ (t)). ϕ '[ ϕ ' (λ)] T TT + M y + ( ψ ( t),..., ψ ( t))[ ϕ ' + ( λ)] TT M y where ϕ = τ / β d M = Σ + λi. If the lt of posteror e vlue s tke for τ, we fd tht ( ϕ + ) l ϕt' TT' M(λ) ϕ ( ) = T M T T M d ' (λ) ' (λ) ( ϕtt + M ) l ' (λ) ϕ ( ( ) ) = M (λ) I T T' M (λ) T T' M (λ) So tht l E ( f ( t) y) = f ( t). Ths result s τ τ detcl wth sple esttor tht obted fro Pelzed Log Lkelhood pproch. Sple esttor s strogly flueced by the soothg preter λ. The ethod used selectg the soothg preter λ for the sple esttor bsed o Byes pproch s GCV. 4. The Ptter of Poverty d Ueployet Relto Idoes A lot of lterture stte tht there s close reltoshp betwee ueployet d poverty, but t s ot esy to prove t eprclly [6]. Ussully the lysts use two dt sources to see ts reltoshp Idoes. Poverty dt re clculted fro the results of Suses (Ntol Socl Ecooc Survey) d ueployet dt re obted fro the Skers (Ntol Lbour Survey). The dffculty to show the reltoshp betwee ueployet d poverty Idoes eprclly, c be solved by usg sple opretrc regresso odel. Accordg to sctter plot Fgure, we c see tht the reltoshp betwee ope ueployet rte d poverty percetge hs o ptter. So tht, the level of poverty Idoes s odeled usg sple opretrc odel where kots pot s selected usg GCV ethod. λ IJBAS-IJENS Deceber 0 IJENS

5 Itertol Jourl of Bsc & Appled Sceces IJBAS-IJENS Vol: No: 06 3 Tble. GCV d MSE vlues t vrous kot pots of the qudrtc sple odel persetse kesk tgkt pegggur terbuk Fgure. Sctter plot betwee ope ueployet rte d poverty percetge Tble, Tble d Tble 3 show the GCV vlues of ech pot of the selected kots. For the ler sple odel, the sllest GCV vlue s correspodg to the kot pots k = 7.4, k = 7.68, d k 3 = For the qudrtc sple odel, the sllest GCV vlue s correspodg to the kot pots k = 3.87 d k = 4.4. Ad for the cubc sple odel, the sllest GCV vlue s correspodg to the kot pots k = d k = Aog those three sple odels, the sllest GCV occurs the qudrtc sple odel by usg kot pots. Tble. GCV d MSE vlues t vrous kot pots of the ler sple odel Nuber of Kot Kot Pots GCV k = k = k = k = k = k = k = 7.4, k = k = 7.4, k = k = 7.4, k = k = 7.4, k = k = 7.4, k = k = 7.4, k = k = 7.4, k = 7.68, k 3 = k = 7.4, k = 7.68, k 3 = k = 7.4, k = 7.68, k 3 = k = 7.4, k = 7.68, k 3 = k = 7.4, k = 7.68, k 3 = k = 7.4, k = 7.68, k 3 = Nuber of Kot Kot Pots GCV k = k = k = k = k = k = k = 3.87, k = k = 3.87, k = k = 3.87, k = k = 3.87, k = k = 3.87, k = k = 3.87, k = k = 3.95, k = 4.4, k 3 = k = 3.96, k = 4.4, k 3 = k = 3.97, k = 4.4, k 3 = k = 3.98, k = 4.4, k 3 = k = 3.99, k = 4.4, k 3 = k = 4.00, k = 4.4, k 3 = Tble 3. GCV d MSE vlues t vrous kot pots of the cubc sple odel persetse kesk Nuber of Kot Kot Pots GCV k = k = k = k = k = k = k = 4.059, k = k = 4.059, k = k = 4.059, k = k = 4.059, k = k = 4.059, k = k = 4.059, k = k = 4.00, k = 4.849, k 3 = k = 4.00, k = 4.850, k 3 = k = 4.00, k = 4.85, k 3 = k = 4.00, k = 4.85, k 3 = k = 4.00, k = 4.853, k 3 = k = 4.00, k = 4.854, k 3 = tgkt pegggur terbuk Fgure. The ler sple wth 3 kots (k = 7.4, k = 7.68, d k 3 = 8.49) IJBAS-IJENS Deceber 0 IJENS

6 Itertol Jourl of Bsc & Appled Sceces IJBAS-IJENS Vol: No: 06 4 persetse kesk persetse kesk Tgkt Pegggur Terbuk Fgure 3. The cubc sple wth kots (k = d k = 7.649) tgkt pegggur terbuk Fgure 4. The qudrtc sple wth kots (k = 3.87 d k = 4.4) Ler sple d cubc sple pproch wth three d two kots respectvely re ot optl yet whch s vsully show Fgure d Fgure 3. Dfferet fro those two prevous sple odels, qudrtc sple estto odel wth two kots s ble to optlly esttes the ptter of dt, so tht behvor of the ptter of chge ech tervl of the ope ueployet rte c be detfed d vsully show by Fgure 4. Qudrtc sple odel wth two kot pots optl t k = 3.87 d k = 4.4 s gve by yˆ( t) = t 04.56t ( t ) ( t ) t 04.56t, t < 3.87 = t 78.96t, 3.87 t < t 0.`t, 4.4 t I 00, the percetge of poverty Idoes hs qudrtc ptter d rse t the ope ueployet rte s less th 3.87, d wll decle whe the ope ueployet rte oved betwee 3.87 d 4.4. After the ope ueployet rte rech 4.4, the percetge of poverty re-ptter qudrtclly but decrese slowly. Bsed o dt fro BPS publcto, the reltoshp betwee the level of ueployet d poverty Idoes does ot follow ptter lke tht foud Kore. The fct tht there s t provcl level whe the ueployet rte creses, the poverty rte s decresg or vce vers (see Fgure ). So the cse of Idoes, the reltoshp betwee ueployet d poverty re ot lwys the se drecto ccordg to the ssupto of exstg ecooc theory, but t hs verse reltoshp. Ths wek ueployet-poverty reltoshp s evdetly see t provcl level. I 00, Idoes whch s cossts of 33 provces, there were soe provces such s Ru, South Klt d North Sulwes, whch ted to hve frly strog reltoshp betwee ueployet d poverty, but the provces such s Ppu, West Ppu, Mluku, West Sulwes, Southest Sulwes, Gorotlo, West Nus Teggr, Est Nus Teggr, d NAD, the poverty rte sees very hgh copred to the level of ueployet. Ths s becuse soe people who work those res re low pd, so tht ther coe s lted or stll below the poverty le. Ths pheoeo s ot oly flueced by the ecooc sde, but socl culturl d geogrphcl codtos lso cotrbuted gretly to the level of poverty. The poverty level Jkrt d Bte, sees too low copred to the level of ueployet. Ths pheoeo c be expled s follows. People who re ble to be ueployed household y dcte tht those household hve suffcet coe to support the ueployed. I ter of poverty, the ueployed those household does ot utotclly becoe poor becuse there re other fly ebers who hve suffcet coe to sust hs fly lve bove the poverty le. I ddto, the fcts show tht urb res there re soe people who volutrly ueployed becuse they re wtg to get the job ccordg to the ther skll or educto, d they re ot relly poor becuse they y be prt of household wth ddle to upper coe. Not oly tht, there re lso y dsgused workers who re ot regstered,.e. coercl sex workers, llegl goods seller, beggrs, etc, who durg the survey cled jobless (ueployed). Ther coes re geerlly bove the poverty le. Those thgs re the cuse of the ueployet rte s IJBAS-IJENS Deceber 0 IJENS

7 Itertol Jourl of Bsc & Appled Sceces IJBAS-IJENS Vol: No: 06 5 cresg rpdly but the rte of poverty s reduced. Aother explto s tht poor households re lost possble to be ueployed [3]. Osh [3] stteet c be uderstood cosderg developg coutres lke Idoes there re o socl securty for ueployed, so order to survve, the poor hve to work, whether they lke or ot, eve oly few hours week. Ths s cosstet wth [4] who sd tht the poor re those who do ot work regulrly or cotuously, or who workg prtte. Streete, et l [4] explctly stted tht ueployet ws ot stsfctory esure of poverty, becuse geerlly people who re ueployed hve better codto, whle ost people who re relly poor t s ot dle. 5. Coclusos The ptter of the reltoshp betwee poverty d ueployet Idoes c be see usg qudrtc sple odels wth two optl kots. Percetge of poverty s qudrtc curve d rse the stge whe ope ueployet rte s less th 3.87, d wll be decled whe the ope ueployet rte oved betwee 3.87 d 4.4. But fter the ope ueployet rte reched 4.4, the percetge of poverty repttered qudrtclly but decresed slowly. So, for the cse Idoes, udrectol reltoshp betwee poverty d ueployet the rego oly prtlly occurred, whle soe re ctully spg. I order to see the effect of ueployet o poverty, we lso eed to look t chrcterstcs of ech rego. It lso eeds to look t other fctors relted to the eployet,.e. feld of busess where he worked, busess sttus (forl / forl), d hours worked per week. So for further reserch c use the Byes Multvrte Sple pproch. 6. Refereces []. Adebyo, S. B., 003, Modellg chldhood lutrto Zb: dptve Byes sples pproch, Sttstcl Methods & Applctos, : 7 4. []. Atods, A., Gregorre, G. d Mckegu, W., 994, Wvelet Methods for Curve Estto, Jourl of the Aerc Sttstcl Assocto, 89, [3]. Atods, A., Bgot, J. d Spts, T., 00, Wvelet Esttors Nopretrc Regresso: A Coprtve Sulto Study, Jourl of Sttstcl Softwre, 6, -83. [4]. Ayd, D., 007. A coprso of the opretrc regresso odels usg soothg sple d kerel regresso. Proc. World Acd. Sc. Eg. Techol., 36 : pdf. [5]. Berry, S.M., Crroll, R.J., d Ruppert, D., 00. Byes soothg d regresso sples for esureet error probles. J. Aer. Sttst. Assoc. 97, [6]. BPS-Sttstcs Idoes, 009, Alyss of Poverty, Eployet d Icoe Dstrbuto, BPS, Jkrt. [7]. BPS-Sttstcs Idoes, 009, Alyss d Clculto of Poverty Level, BPS, Jkrt. [8]. Budtr, I. N., Subr, d Soejoet, Z., 997, Weghted Sple Esttor, Bullet of the Itertol Sttstcl Isttute, 5, [9]. Budtr, I. N., d Subr, 998, Byes Approch To Nopretrc Sple Curves Weghted Regresso, Jourl of Mthetcs Assocto of Idoes (MIHMI), 4, [0]. Budtr, I. N., 000, Method U, GML, CV d GCV Nopretrc Sple Regresso, Jourl of Mthetcs Assocto of Idoes (MIHMI), 6, []. Budtr, I. N., 00, Pelzed Lkelhood Type Esttor, Jourl of Nturl Ubrw Mthetcs d Nturl Sceces, Specl Issue, []. Budtr, I. N., 005, Tructed Polyol Sple Model Fly I sepretrc regresso, Ppers of the Ntol Ser o Mthetcs, Mthetcs Deprtet Dpoegoro Uversty, Serg. [3]. Budtr, I. N., 006, Sple Models Wth Optl Kots, Jourl of Bsc Scece, Mthetcs d Nturl Sceces Uversty of Jeber, 7, [4]. Chb, S., d Greeberg, E., 00. Addtve cubc sple regresso wth Drchlet process xture errors. Jourl of Ecooetrcs 56, IJBAS-IJENS Deceber 0 IJENS

8 Itertol Jourl of Bsc & Appled Sceces IJBAS-IJENS Vol: No: 06 6 [5]. Choudhur N, Ghosl S, d Roy A, 007, Nopretrc bry regresso usg Guss Process Pror, Sttstcl Methodology, 4, 7-43 [6]. Cox, D. D. d O Sullv, F.,996, Pelzed Type Esttor for Geerlzed Nopretrc Regresso, 983, Jourl of Multvrte Alyss, 56, [7]. Crceu, C., Ruppert, D. d Wd, M.P, 005. Byes lyss for pelzed sple regresso usg WBUGS. Jourl of Sttstcl Softwre, Volue 4, Artcle 4. [8]. Crve, P., d Whb, G., 979, Soothg Nosy Dt Wth Sple Fuctos, Nuersche Mthetk, 3, [9]. de Boor, C, 978, A Prctcl Gude to Sples, Sprger-Verlg. [0]. DeF, R., 00, The Ipct of Mcroecooc Perforce o Altertve Poverty Mesures, Socl Scece Reserch, 3: []. Eubk,R.L.,988, Sple Soothg d Nopretrc Regresso, Mercel Dekker, New York. []. Fred, J., 99, Multvrte Regresso d Sple Soothg, A. Sttst 9, -4. [3]. Gree, P. J. d Slver, B.W., 994, Nopretrk Regresso d Geerlzed Ler Models ( Roughess Pelty Approch), Chp & Hll, New York. [4]. Gu, C., (99), Pelzed Lkelhood Regresso: A Byes Alyss, Sttstc Sc, [5]. Hrdle, G., 990, Appled Nopretrk Regresso, Cbrdge Uversty Press, New York. [6]. Holes, C. C. d Mllck, B. K., 00, Byes regresso wth ultvrte ler sples, J. Roy. Sttst Soc. B, 63, (), 3-7. [7]. Keldorf, G. d Whb, G., 970, A correspodece betwee Byes estto o stochstc processes d soothg by sples, A. Mth. Sttst., 4, [8]. Keldrof, G. d Whb, G., 97, Soe Result o Tchebycheff Sple Fucto, Jourl of Mthetcl Alyss d Applcto, 33, [9]. Koeker, R., Ng., P. d Portoy, S.,994, Qutle Soothg Sple, Boetrk, 8, [30]. Oehlert, G.W.,99, Relxed Boudry Soothg Sple, The Als of Sttstcs, 0, [3]. Osh, Hrry T., 990, Eployet Geerto: The Log-Ter soluto to Poverty. As Developet Revew. Vol. 8. No.. [3]. Prk, A. Wg, S d Wu, G., 00, Regol Poverty Trgetg Ch, Jourl of Publc Ecoocs, Vol 86 pp3-53. [33]. Suders, P., 00, The Drect d Idrect Effects of Ueployet o Poverty d Iequlty, SPRC Dscusso Pper No. 8, The Socl Polcy Reserch Cetre Uversty of New South Wles, Sydey NSW 05, Austrl. [34]. Slver, B., 984, A Fst d Effcet Cross-Vldto Method for Soothg Preter Choce Sple Regresso, Jourl of the Aerc Sttstcl Assocto, 79, [35]. Slver, B., 985, Soe Aspects of the sple Soothg Approch to No Pretrc Regresso Curve Fttg (Wth Dscusso), Jourl Royl Sttstcl Socety, 47, -5. [36]. Sth, M. d Koh, R., 997, A Byes Approch Bvrte Regresso, Jourl of the Aerc Sttstcl Assocto, 9, [37]. So, H. H. d Kkw, N., 006, Mesurg the pct of prce chges o poverty: w th pplctos to Thld d Kore, Jourl of Ecooc Iequlty, Vol. 4, No., [38]. Speck, P., 980, Mx Esttes of Ler Fuctols Hlbert Spce, Upublshed Muscrpt. [39]. Speck, P., 985, Sple Soothg d Optl Rtes of Covergece Nopretrc Regresso Models, Jourl A. Sttst, 3, [40]. Speck, P., 988, Kerel soothg prtl ler odels. J. Roy. Sttst. Soc. Se. B 50 (3), [4]. Streete, Pul, Burk, S.J., Hq, M., Hcks, N., d Stewrt, F., 98, Frst Thgs Frst, Meetg Bsc Hu Needs Developg Coutres, New York: Oxford Uversty Press IJBAS-IJENS Deceber 0 IJENS

9 Itertol Jourl of Bsc & Appled Sceces IJBAS-IJENS Vol: No: 06 7 [4]. Todro, M.P Ecooc Developet, 6 th edto, New York: Log, chpter 5. [43]. Verbeek, M., 008. A Gude to Moder Ecooetrcs, thrd ed. Joh Wley & Sos, Ltd., Chchester. [44]. Whb, G., 978, Iproper prors, sple soothg d the proble of gurdg gst odel errors regresso, Jurl Royl Sttstcs Socety, B, 40, [45]. Whb, G., 983, Byes "Cofdece Itervls" for the crossvldted soothg sple, Jurl Royl Sttstcs Socety, B, 45, [46]. Whb, G., 985, A Coprso of GCV d GML for Choosg the Soothg Preter the Geerlzed Sple Soothg Proble, Jourl the Als of Sttstcs, 3, [47]. Whb, G., 990, Sple Model for Observtol Dt, Socety For Idustrl d Appled Mthetcs, Phldelph. [48]. Whb, G., 000, A Itroducto to Model Buldg wth Reproducg Kerel Hlbert Spces, Techcl Report, 00, Uversty of Wscos, 97, IJBAS-IJENS Deceber 0 IJENS