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\begin{array}{rcl} \hat{Var} (\hat{V}) & = & {(\frac{n - 1}{n})}^{2} \frac{1}{M} \hat{Var} (s_{m}^{2}) + {(\frac{M + 1}{n M})}^{2} \frac{2}{M - 1} B^{2} \\ + 2 \frac{(M + 1) (n - 1)}{n^{2} M} \frac{n}{M} (\hat{cov} (s_{m}^{2}, ({\bar{θ}}_{m}^{\cdot})^{2}) - 2 {\bar{θ}}_{\cdot}^{\cdot} \hat{cov} (s_{m}^{2}, {\bar{θ}}_{m}^{\cdot})) \end{array}

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\begin{eqnarray*} \widehat{\textrm{Var}} (\widehat{V}) & =& \left( \frac{n-1}{n} \right)^2 \frac{1}{M} \widehat{\textrm{Var}}(s_ m^2) + \left( \frac{M+1}{nM} \right)^2 \frac{2}{M-1} B^2 \\ & & + ~ 2\frac{(M+1)(n-1)}{n^2M} \frac{n}{M} \left( \widehat{\textrm{cov}}(s_ m^2, (\bar{\theta }_ m^{\cdot })^2) - 2 \bar{\theta }_{\cdot }^{\cdot } \widehat{\textrm{cov}}(s_ m^2, \bar{\theta }_ m^{\cdot }) \right) \end{eqnarray*}