Unbiased estimates of the variance components: The one-way model. Using (2.21) and (2.22), show that (Eleft(widehat{sigma}_{1}^{2}ight)=sigma_{1}^{2}) and

Question:

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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