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InDina [[statisticsstatistik]] the, '''mean squaredkuadrat errorkasalahan''' of antina [[estimator]] ''T'' ofdina anparameter unobservablenu parameterteu ka-observasi θ isnyaeta
:<math>\operatorname{MSE}(T)=\operatorname{E}((T-\theta)^2),</math>
dina hal ieu, ngarupakeun nilai ekspektasi kuadrat "kasalahan". "Kasalahan" nyaeta jumlah numana estimator beda jeung jumlah nu keur di-estimasi. Mean kuadrat kasalahan nyukupan identitas
i.e., it is the expected value of the square of the "error". The "error" is the amount by which the estimator differs from the quantity to be estimated. The mean squared error satisfies the identity
:<math>\operatorname{MSE}(T)=\operatorname{var}(T)+(\operatorname{bias}(T))^2</math>
dimana
where
:<math>\operatorname{bias}(T)=\operatorname{E}(T)-\theta,</math>
i.e.dina hal ieu, the [[bias (statistics)|bias]] isnyaeta thelobana amountnumana bynilai whichekspektasi thetina expectedestimator valuebeda ofkeur thejumlah estimator differs from thenu unobservableteu quantityka-observasi tonu bekeur estimateddi-estimasi.
Conto kongkritna. Anggap
Here is a concrete example. Suppose
:<math>X_1,\dots,X_n\sim\operatorname{N}(\mu,\sigma^2),</math>
i.e.dina hal ieu, thisukran is asampel random sample of size ''n'' fromtina apopulasi [[sebaran normal distribution|normally distributed]] population. TwoDua estimators of σ<sup>2</sup> are sometimeskadangkala useddipake (asatawa arenu otherssejenna):
:<math>\frac{1}{n}\sum_{i=1}^n\left(X_i-\overline{X}\,\right)^2\ {\rm and}\ \frac{1}
{n-1}\sum_{i=1}^n\left(X_i-\overline{X}\,\right)^2 </math>
numana
where
:<math>\overline{X}=(X_1+\cdots+X_n)/n</math>
is thengarupakeun "samplesampel mean". TheKahiji firsttina ofestimator theseieu estimatorsnyaeta is theestimator [[maximum likelihood]], estimatorsarta bias, anddina ishal biasedieu, i.e.,bias its biasteu issarua notjeung zeronol, buttapi hasngabogaan avarian smallernu varianceleuwih thanleutik thetinimbang secondnu kadua, whichanu isteu unbiasedbias. TheVarian smallerleutik variancetina compensatesakibat somewhatsejen for thekeur bias, so that themangka mean squaredkuadrat errorkasalahan oftina the biasedbias estimator isleuwih slightlyleutik smallertinimbang than that of theestimator unbiased estimator.
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