C = σ_{int}^{2} + σ_{m}^{2} + σ_{C}^{2}, H = σ_{int}^{2} + σ_{m}^{2} .

Then

M_{0} = \overset{q}{ˉ}

and

θ = \overset{q}{ˉ} - \overset{r}{ˉ}

Cov (M_{0} θ) = (C / K C / K C / K C / K + H / N) .

I (M_{0}, θ) = (K / C + N / H - N / H - N / H N / H),

and its inverse is exactly the displayed covariance matrix. The estimators therefore attain the multivariate Cramer-Rao bound and are efficient estimators.

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