samanyikrut kiman chauras

sankhyikimadhye, samanyikrut kiman varg (jee. ell. ess.) hii eka paddhat aahe jee rekheey pratigaman modelmadhil adnyat mapdandancha andaj lavnyasathi vaparali jaate jevha pratigaman modelmadhil avashishtanmadhye vishisht pramanat parasparsambandh asato. kiman chauras aanee vajandar kiman chauras heey sankhyikiyadrushtya adhik karyaksham asane aanee dishabhul karnare nishkarsh talhane aavashyak asoo shakate. glussche varnan pahilyanda alekzandar etken yanni 1935 madhye kele hote.
paddhatichi ruparesha.
manak resheey pratigaman pratimananmadhye, "aine" sankhyikeey ekkanvar deta sootra _ _ nirikshan kele jaate. pratisad moolye vector sootra _ 2 madhye thewali jaatat aanee predictor moolye rachana matricks sootra _ 3 madhye thewali jaatat, jethe sootra _ 4 haah "i" vya ekkasathi "k" predictor chalancha (sthirankansah) vector aahe. heey model dilelya sootra _ 5 chey sashart sarasari sootra _ 6 chey resheey karya mhanoon sakti karate aanee dilelya truti sandnyeche sashart bhinnata sootra _ 6 heey "dnyat" nonsingular "covarians matricks" sootra aahe asey gruheet dharate. heey sahasa asey lihile jaate
yethe sootra _ 11 heey adnyat sthirankanche (jyala "pratigaman gunank" mhanoon olakhale jaate) vector aahe jyacha andaj detavarun lavala jaane aavashyak aahe.
samaja sootra _ 12 haah sootra _ 13 sathee umedvar andaj aahe. tarr sootra _ 12 sathee avashisht vector sootra _ 15 asel. samanyikrut kiman varg paddhat yaa avashisht vectorchi varg mahalanobis lambi qamee karoon sootra _ 13 chaa andaj lavteh
jethe shevatchya done sandnyanche moolyankan scalarmadhye kele jaate, parinami
heey uddisht sootra _ 12 madheel eka dvighat swaroop aahe.
sootra _ 12 chya sandarbhat yaa vargakar swarupacha pravanata ghene aanee tyachi shoonyashi barobari karane (jevha sootra _ 21) dete
mhanoon, spasht sootra dett vastunishtha karyachi kiman ganana kelee jaau shakateh
pariman sootra _ 24 laa 'achook matricks' (kinwa 'dispersion matricks') mhanoon olakhale jaate, jeey karn vajan matrixche samanyikaran aahe.
malmatta.
jee. ell. ess. andajak heey sootra _ 25 aanee sootra _ 26 saha nihpakshapati, susangat, karyaksham aanee lakshanrahitpane samanya aahe. jee. ell. ess. heey detachya resheey rupantarit aavruttivar samanya kiman varg lagoo karnyaitakech aahe. heey pahanyasathi, ghatak sootra _ 27, udaharanarth, cholesky vighatan vaparoon. mug jarr eka sootra _ 28 chya donhi bajunna sootra _ 29 neey purv-gunakar karat asel, tarr aaplyala eka samatulya rekheey model sootra _ 30 milate jethe sootra _ 31, sootra _ 32 aanee sootra _ 33. yaa model sootra _ 34 madhye, jethe sootra _ 35 haah olakh matricks aahe. asha prakare rupantarit mahitivar samanya kiman varg (oo. ell. ess.) lagoo karoon sootra _ 13 chaa karyakshamatene andaj lavala jaau shakato, jyasathi qamee karane aavashyak aaheh
yacha parinam trutinche praman pramanit karane aanee tyancha 'paraspar sambandh todane' assa hoto. jevha samalingi trutinsah deta varr oo. ell. ess. lagoo kele jaate, tevha goss-markov pramey lagoo hoto aanee mhanoon jee. ell. ess. andaj haah "β" sathee sarvottam resheey nihpakshapati andajak asato.
vajan kiman chauras.
jevha 'ω' chya serve auph-diagonal nondi 0 asatat tevha 'waited least squares' (doubleu. ell. ess.) navache jee. ell. ess. chey eka vishesh prakaran udbhavate. hii paristhiti tevha udbhavate jevha nirikshan kelelya mulyanche farak asman asatat kinwa jevha heterocedasticity asate parantu nirikshan kelelya farkanmadhye konatehi parasparsambandh astitvat nasatat. ekak "i" sathiche vajan heey ekak "i" sathichya pratisadachya bhinnatechya paraspar pramananusar asate.
x chey vyavharya samanyikrut kiman varg.
jarr truti sootra 38 chee sahparivartan adnyat asel, tarr vyavharya samanyikrut kiman varg (eff. jee. ell. ess.) andajak mhanoon olakhalya jaanarya jee. ell. ess. chee amalbajavani karnyayogya aavrutti vaparoon sootra 38 chaa susangat andaj miloo shakato, samaja sootra 40. 
eff. jee. ell. madhye, modelling done tappyanmadhye pudhe jaateh 
(1) modelcha andaj oo. ell. ess. kinwa itar susangat (parantu akaryaksham) andajkartyadvare lavala jaato aanee urvaritancha vapar truti sahparivartan matrixcha susangat andaj tayar karnyasathi keela jaato (asey karnyasathi, ekhadyala anekada atirikt maryada maryada modelche parikshan karane aavashyak asate; udaharanarth, truti velechya malikechya prakriyeche anusaran karat asalyas, sankhyikishastradnyala samanyatah yaa prakriyevar kahee saiddhantik gruhitakanchi aavashyakta asate jenekarun satatyapurn andajak upalabdh aahe heey sunishchit karata yeil); aanee 
(2) trutinchya sahparivartan matrixcha susangat andajak vaparoon, ekhadi vyakti jee. ell. ess. kalpana amalat aanoo shakate.
heterocedasticity (heteroskedesticity asehi mhatale jaate) kinwa autocoralation antargat jee. ell. ess. heey oo. ell. peksha adhik karyaksham asale taree, heey eff. jee. ell. sathee kharey nahee. vyavharya andajak haah "lakshanrahitpane" adhik karyaksham aahe, jarr truti sahparivartan matrixcha satatyane andaj lavala gela asel, parantu lahan teey madhyam aakarachya namunyasathi, too pratyakshat oo. ell. ess. peksha qamee karyaksham asoo shakato. mhanunach kahee lekhak oo. ell. vaparnyas pradhanya detat aanee heterocedasticity kinwa syrial autocorylationshi majboot asalelya andajkachya bhinnatesathi paryayi andajakacha vichar karoon tyanche nishkarsh punha tayar karatat.
tathapi, mothya namunyansathi heteroskedesticity kinwa syrial correlation antargat oelpeksha fgla pradhanya dile jaate. eka savadhgirichi nond ashee aahe qee eff. jee. ell. ess. andajak nehmich susangat nasato. jarr vaiyaktik vishisht sthir parinam asateel tarr eff. jee. ell. visangat asoo shakatat.
sarvasadharanpane yaa andajkamadhye jee. ell. ess. peksha bhinn gunadharm aahet. mothya namunyansathi (i.eae.lakshanrahitpane) serve gunadharm jee. ell. ess. chya sandarbhat (yogya paristhitit) samanya aahet, parantu maryadit namunyansathi eff. jee. ell. ess. andajakanche gunadharm adnyat aaheth teey pratyek vishisht modelnusar natakiyaritya badaltat aanee samanya niyam mhanoon tyanche achook vitaran vishleshanatmakapane ghetale jaau shakat nahee. maryadit namunyansathi, kahee prakarananmadhye oo. ell. ess. peksha eff. jee. ell. qamee karyaksham asoo shakatat. asha prakare, jee. ell. ess. vyavharya kele jaau shakate, parantu namuna lahan asatana hii paddhat lagoo karane nehmich shahanpanache nasate.
maryadit namunyanmadhil andajkartyanchi achookata sudharanyasathi vaparali jaanari eka paddhat mhanje punaravrutti karane, i.eae., truti sahparivartan andajak adyayavat karnyasathi eff. jee. ell. kadoon avashisht ghene aanee nantar eff. jee. ell. andaj adyayavat karane, joparyant andajak kahee sahishnutepeksha qamee badalat naheet toparyant teech kalpana punaravruttinusar lagoo karane. parantu mool namuna lahan asalyas hii paddhat andajkartyachi karyakshamta phaar sudharat nahee.
jevha namune khoop mothe nasatat tevha oo. ell. lagoo karane haah eka vajvi paryay asato, parantu shastriy bhinnata andajak kadhoon takane
(jeey yaa chaukatit visangat aahe) aanee tyaeivaji etch. aii. see. (heteroskedesticity aanee autocoralation susangat) andajak vapara. udaharanarth, svayamsambandhanchya sandarbhat aapan bartlet andajak vaparu shakato (bahutekda nyu-west andajak andajak mhanoon olakhala jaato kaaran yaa lekhakanni tyanchya 1987 chya "econometrica" lekhat arthshastradnyanmadhye yaa andajakacha vapar lokpriy keela aahe) aanee vishamsambandhit sandarbhat aapan aaykar-white andajak vaparu shakato. haah drushtikon adhik surakshit aahe aanee namuna motha naslyas too yogya marg aahe, jethe 'motha' hii kadhikadhi nisaradi samasya asate (udaa.jee. trutiche vitaran asamamiteey asalyas aavashyak namuna khoop motha asel).
samanya kiman varg (oo. ell. ess.) andajak asha prakare mojala jaatoh
aanee avashisht sootra _ 43 chey andaj tayar kele jaatat.
sadhepanasathi, heterocedastic aanee gair-autocorated trutinsathi modelcha vichar qaraa. asey gruheet dhara qee truti vectorche bhinnata-sahparivartan matricks sootra _ 44 karn aahe, kinwa samanpane qee bhinn nirikshananmadhil truti parasparsambandhit naheet. mug pratyek karn praveshala basavalelya avashisht sutradvare andaj lavala jaau shakato, tyamule sootra 46 heey asey tayar kele jaau shakateh
heey lakshat ghene mahatvache aahe qee mageel abhivyaktimadhye varg avashisht vaparale jaau shakat naheet; aaplyala trutinchya farkancha andaj lavnara havah aahe. asey karnyasathi, aapan parametric heteroskedecity model kinwa naun parametric estimator vaparu shakato. ekada hii payari purn jhaali qee, aapan pudhe jaau shakatoh
bharit kiman chauras vaparoon sootra _ 49 vaparoon sootra _ 48 chaa andaj lava
prakriya punaravrutti kelee jaau shakate. pahili punaravrutti dilee jaate
sootra _ 54 chaa haah andaj abhisaranat punaravrutti keela jaau shakato.
niyamitatechya paristhitit eff. jee. ell. ess. andajak (kinwa tyachya punaravrutticha andajak, jarr aapan maryadit sankhyene punaravrutti kelee tarr) lakshanrahitpane asha prakare vitarit keela jaatoh
jethe n haah namuna aakar aahe aanee
yethe pii-liim mhanje sambhavyatechi maryada.

