# Isbarbardhigga Stein1122

Sannadkii 1961-kii James iyo Stein waxay daabaceen warqadda Qiyaasta oo leh Khasaaraha Quadratic . Qaado xogta sida caadiga ah loo qaybiyey oo leh micne aan la garanayn $$\mu$$ iyo kala duwanaansho $$1$$ . Haddii aad hadda ka doorato qiime random $$x$$ xogtan oo ay tahay inaad qiyaasto celceliska $$\mu$$ taas oo ku saleysan tan, dareen $$x$$ waa qiyaas macquul ah $$\mu$$ (maadaama qaybinta caadiga ahi jirto, si bakhtiyaa nasiib ah loo doortay $$x$$ waxay u dhowdahay $$\mu$$ ).

Hadda tijaabadii waa lagu soo noqnoqday - markan oo leh saddex madax-bannaan, mar labaad si caadi ah loo qaybiyey xogta waxay mid kastaaba kala duwan tahay $$1$$ iyo celceliska qiyamka $$\mu_1$$ , $$\mu_2$$ , $$\mu_3$$ . Kadib markii la helo saddex qiime oo random $$x_1$$ , $$x_2$$ iyo $$x_3$$ , hal qiyaas (iyadoo la isticmaalayo hab isku mid ah) $$\mu_1=x_1$$ , $$\mu_2=x_2$$ iyo $$\mu_3=x_3$$ .

Natiijada la yaabka leh ee James iyo Stein ayaa ah in ay jirto qiyaas ka wanaagsan $$\left( \mu_1, \mu_2, \mu_3 \right)$$ (ie isku darka saddexda xog ee madaxbannaan) marka loo eego $$\left( x_1, x_2, x_3 \right)$$ . "James Stein estimator" waa markaa:

$$\begin{pmatrix}\mu_1\\\mu_2\\\mu_3\end{pmatrix} = \left( 1-\frac{1}{x_1^2+x_2^2+x_3^2} \right) \begin{pmatrix}x_1\\x_2\\x_3\end{pmatrix} \neq \begin{pmatrix}x_1\\x_2\\x_3\end{pmatrix}$$

Celceliska leexashada labajibbaaran ee qiyaasahan ayaa markaa had iyo jeer ka yar celceliska leexashada labajibbaaran $$E \left[ \left|| X - \mu \right||^2 \right]$$

Waa wax lala yaabo oo laga yaabo inay is-barbar-dhigaan in qiyaasaha James-Stein uu u beddelo qiyaasaha caadiga ah (wax yar oo sii yaraanaya) xagga asalka oo uu sidaas ku keeno natiijo wanaagsan inta badan kiisaska. Tani waxay khusaysaa cabbirrada $$\geq 3$$ , laakiin kuma jiraan kiiska laba-geesoodka ah.

Sharaxaad joomatari wanaagsan oo ku saabsan sababta tani u shaqeyso waxaa bixiya Brown & Zao . Ogsoonow in tani aysan macnaheedu ahayn inaad leedahay qiyaas ka wanaagsan mid kasta oo xog ah - waxaad haysataa qiyaas ka wanaagsan oo leh khatar yar oo la isku daray .

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