
olakh patvane

sankhyikimadhye, olakhata yene haah eka gunadharm aahe jyache achook nishkarsh shakya honyasathi pratimanane samadhan karane aavashyak aahe. yaa pratimechya moolbhut mapdandanchi kharee moolye jaanun ghene saiddhantikdrushtya shakya asalyas, tyatoon asankhya nirikshane midalyanantar, pratimechi olakh patavata yete. ganitiyadrushtya, heey asey mhananyaitakech aahe qee parameterschya vegvegalya moolyanni nirikshan karnyayogya chalanche vegvegale sambhavyata vitaran nirman karane aavashyak aahe. samanyatah model keval kahee tantrik nirbandhankhali olakhata yete, asha paristhitit yaa aavashyaktanchya sanchala olakh atty mhanatat.
jeey model olakhanyayogya nahee teey olakhanyayogya nahee kinwa olakhanyayogya nahee asey mhatale jaateh done kinwa adhik parametrizations nirikshanatmakdrushtya samatulya asatat. kahee prakarananmadhye, jaree ekhade model olakhanyayogya nasale taree, model parameterschya vishisht upasanchachi kharee moolye jaanun ghene ajunahi shakya aahe. yaa prakaranat aamhi mhanato qee model anshatah olakhanyayogya aahe. itar prakarananmadhye, parameter spacemadhil vishisht maryadit kshetraparyant khyan parametres sthan jaanun ghene shakya asoo shakate, asha paristhitit model olakhanyayogya seet kele jaate.
modelchya gunadharmanchya katekorpane saiddhantik shodhavyatirikt, jevha ekhadya modelchi chachani prayogik deta sanchansah, olakhanyayogyateche vishleshan vaparoon kelee jaate tevha olakhanyayogyatecha sandarbh vyapak vyaptimadhye deela jaau shakato.
vyakhya.
sootra _ 1 heey antaral sootra _ 2 yaa mapdandasah eka sankhyikeey model asoo dya. aapan mhanato qee jarr mapping sootra _ 4 eka-eka asel tarr sootra _ 3 olakhanyayogya aaheh
yaa vyakhyecha arth assa aahe qee "θ" chee bhinn moolye vishisht sambhavyata vitarananshi sambandhit asali pahijetah jarr "θ" 1 ≤ "θ" 2, tarr "p" "θ" 1 ≤ "p" θ "2. jarr vitaran sambhavyata ghanata karyanchya (pdfs) drushtine paribhashit kele gele asel, tarr done pdfs heey shoonya nasalelya mojamapachya sanchavar bhinn asateel tarach vegale manale pahijet (udaharanarth done karye φ1 (" x ") = 10 ≤" x "<1 aanee φ2 (" x ") = 10 ≤" x "≤ 1 keval ekach binduvar bhinn asatat-mojamapache sanch shoonya-aanee tyamule teey bhinn pdfs manale jaau shakat naheet).
nakashatil sootra 4 chya ulatpanachya arthane modelchi olakh patvane heey modelche kharey mapdand jaanun ghenyas saksham asanyaitkech aahe, jarr model anishchit kalaparyant nirikshanat thevata aale. kharokhar, jarr {"xt" "s" haah pratimanatil nirikshanancha kram asel, tarr mothya sankhyanchya majboot niyamapramane,
pratyek mojata yenyajogya sanchasathi "aaa" Â "s" (yethe 1 {...} heey soochak karya aahe). asha prakare, asankhya nirikshanansah aapan modelmadhye kharey sambhavyata vitaran "p" 0 shodhu shakoo aanee vareel olakhanyachi sthitisathi nakasha sootra _ 4 ulat karane aavashyak asalyane, aapan vitaran "p" 0 dilelya parametres kharey moolya dekhil shodhu shakoo.
udaharane.
udaharan 1.
sootra _ 3 heey samanya sthan-praman kutumb asoo dyah
mug
hii abhivyakti jawaljawal serve "x" sathee shoonyachya barobarichi asate, jevha tyache serve gunank shoonyachya barobariche asatat, jeey tevhach shakya aahe jevha ."σ" 1. = ."σ" 2. aanee "microsoft" 1 = "microsoft" 2. scale parametermadhe "microsoft" shoonyapeksha mothe asane pratibandhit asalyane, aapan assa nishkarsh kadhatoh model olakhanyayogya aaheh f "θ" 1 = f "θ" 2 "θ" 1 = "θ" 2.
udaharan 2.
sootra _ 3 heey manak resheey pratigaman model asoo dyah
(jethe 'heey matricks transpose darshavate). jarr aanee keval matricks sootra _ 14 ulat karata yenyajoge asel tarach 'β' haah mapdand olakhata yeto. asha prakare, hii modelmadhil olakhanyachi aut aahe.
udaharan 3.
samaja sootra _ 3 heey shastriy truti-inn-variables resheey model aaheh
jethe ("ε", "η", "x *") heey sanyuktapane shoonya apekshit moolya aanee adnyat farkansah samanya swatantra yadruchchik chull aahet aanee keval chull ("x", "y") disun yetat. mug heey model olakhanyayogya nahee, fakt utpadan βσ2 ≤ aahe (jethe σ2 ≤ haah supt pratigami "x *" chaa farak aahe). heey dekhil olakhanyayogya sanch pratikrutiche eka udaharan aaheh jaree 'β' chey achook moolya shikale jaau shakat nasale taree, teey madhyantaramadhye kuthetari asale pahije ('β' yx, 1 ρ 'β' xy), jethe 'β' yx haah 'x' varr 'y' chya oo. ell. ess. pratigamanatil gunank aahe aanee 'β' xy haah 'y' varr 'x' chya oo. ell. ess. pratigamanatil gunank aahe.
jarr aapan samanyatechi dharana sodoon dilee aanee fakt 'ε' η 'η' x * 'hii swatantra aut rakhoon' x * 'samanyatah vitarit kele gele naheet ashee aavashyakta asel, tarr model olakhanyayogya hote.