Unbiased estimates of the variance components: The one-way model. Using (2.21) and (2.22), show that \(E\left(\widehat{\sigma}_{1}^{2}ight)=\sigma_{1}^{2}\) and \(E\left(\widehat{\sigma}_{v}^{2}ight)=\sigma_{v}^{2}\), Hint: \(E\left(u^{\prime} Q uight)=\) \(E\left\{\operatorname{tr}\left(u^{\prime} Q uight)ight\}=E\left\{\operatorname{tr}\left(u u^{\prime} Qight)ight\}=\operatorname{tr}\left\{E\left(u u^{\prime}ight) Qight\}=\operatorname{tr}(\Omega Q)\).

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of = of = u' Qu tr(Q) u' Pu tr (P) = -=Tu/N i=1 (Uit - .) Ziel N(T-1) t=1 (2.21) (2.22)