\begin{table}
    \centering
\begin{tabular}{l l l l l r l}
	 exh 	&  Type 	&  Reference & Formula\\ \toprule
			
     yes 	&  \psynthetic{} 	& \analogy{} & $\hat{Y}_{c,G,synth} = \bar{Z}^t_G\hat{\beta}_{c,s_2}$ \\
	   	&    	& \analogy{} & $\hat{V} = \bar{Z}^t_G \hat{\Sigma}_{ \hat{\beta}_{s_2}} \bar{Z}_G $\\
\lightrule
			
yes 	&  \psmall{} 	& \analogy{} & $ \hat{Y}_{c,G,small} = \hat{Y}_{c,G,synth} + \mRc$\\
	   	&    	& \analogy{} & $  \hat{V} = \hat{V}\left(\hat{Y}_{c,G,synth}\right) + \vRc$ \\
\lightrule

yes 	&  \pextended{} 	& \cite[eq. 48]{Man13a} & $ \hat{\tilde{Y}}_{c,G,synth} = \bar{\eZ}^t_G\hat{\theta}_{c,s_2}$ \\
    &    	& \cite[eq. 49]{Man13a} & $ \hat{V} = \bar{\eZ}^t_G \hat{\Sigma}_{ \hat{\theta}_{c,s_2}} \bar{\eZ}_G$ \\
			
\strongrule
no 	&  \psynthetic{} 	& \cite[eq. 42]{Man13a} & $ \hat{Y}_{c,G,psynth} = \hat{\bar{Z}}^{1}_{c,s_1,G} \hat{\beta}_{c,s_2}$ \\
        &    	& \cite[eq. 43]{Man13a} & $ \hat{V}(\dot) =\hat{\bar{Z}}^t_{c,s_1,G} \hat{\Sigma}_{ \hat{\beta}_{c,s_2}} \hat{\bar{Z}}_{c,s_1,G} + \hat{\beta}^t_{c,s_2} \hat{\Sigma}_{ \hat{\bar{Z}}_{c,s_1,G}  } \hat{\beta}_{c,s_2} $ \\
\lightrule
			
no 	&  \psmall{} 	& \cite[eq. 44]{Man13a} & $ \hat{Y}_{c,G,psmall} = \hat{Y}_{c,G,psynth} + \mRc$ \\
            &      	& \cite[eq. 45]{Man13a} & $ \hat{V} = \hat{V}\left(\hat{Y}_{c,G,psynth}\right) + \vRc$ \\
\lightrule
no 	&  \pextended{} 	& \cite[eq. 46]{Man13a} & $ \hat{\tilde{Y}}_{c,G,psynth} = \hat{\bar{\eZ}}^t_{c,s_1,G}\hat{\theta}_{c,s_2}$ \\
    &    	&  \cite[eq. 47]{Man13a} & $ \hat{V} = \hat{\bar{\eZ}}^t_{c,s_1,G} \hat{\Sigma}_{ \hat{\theta}_{c,s_2}} \hat{\bar{\eZ}}_{c,s_1,G} + \hat{\theta}^t_{c,s_2} \hat{\Sigma}_{ \hat{\bar{\eZ}}_{c,s_1,G}  } \hat{\theta}_{c,s_2}$ \\
			
			
\strongrule
part 	&  \psynthetic{} 	& \analogy{} & $\hat{Y}_{c,psynth, G,greg} = \left(
\bar{Z}_G^{(1)}- \hat{\bar{Z}}_{c,s_1,G}^{(1)}\right) \hat{\alpha}_{c,2} + \hat{\bar{Z}}^t_{c,s_1,G}\hat{\beta}_{c,s_2}  $\\
	   	&    	&     \analogy{} & $ \hat{V} = \frac{n_{s_2}}{n_{s_1}}\bar{Z}^{(1)t}_G \hat{\Sigma}_{ \hat{\alpha}_{c,s_2}} \bar{Z}^{(1)}_G + (1-\frac{n_{s_2}}{n_{s_1}})\hat{\bar{Z}}^{t}_{c,s_1,G} \hat{\Sigma}_{ \hat{\beta}_{c,s_2}} \hat{\bar{Z}}_{c,s_1,G} $\\
\lightrule
			
part 	&  \psmall{} 	& \analogy{} & $ \hat{Y}_{c,G,greg} = \hat{Y}_{c,G,psynth} + \mRc $\\
	    	&      	& \analogy{} & $ \hat{V}  = \hat{V}\left(\hat{Y}_{c,psynth, G,greg}\right)  + \vRc$\\
\lightrule
part 	&  \pextended{} 	& \cite[eq. 50]{Man13b.e} & $\hat{\tilde{Y}}_{c,G,greg} = \left( \bar{\eZ}_G^{(1)}- \hat{\bar{\eZ}}_{c,s_1,G}^{(1)}\right) \hat{\gamma}_{c,2} + \hat{\bar{\eZ}}^t_{c,s_1,G}\hat{\theta}_{c,2} $\\
        &    	&     \cite[eq. 52]{Man13b.e} &$\hat{V} = \frac{n_{s_2}}{n_{s_1}}\bar{\eZ}^{(1)t}_G \hat{\Sigma}_{ \hat{\gamma}_{c,s_2}} \bar{\eZ}^{(1)}_G + (1-\frac{n_{s_2}}{n_{s_1}})\hat{\bar{\eZ}}^{t}_{c,s_1,G}
\hat{\Sigma}_{ \hat{\theta}_{c,s_2}} \hat{\bar{\eZ}}_{c,s_1,G} $\\
\end{tabular}
\caption{Predictors for clustered two-phase sampling, 
    \emph{exh} denotes exhaustiveness of auxiliary information (yes/no/part, the
    latter meaning partially exhaustive auxiliary information),
    \emph{Type} denotes the area estimator (\psynthetic{} for synthetic, \psmall{}
    for small and \pextended{} for extended synthetic. \emph{Reference} gives the
    refenerce where found, else I derived them by analogy. \label{tab:clustered2}
}
\end{table}
\begin{table}
    \fontsize{8}{2}\selectfont
    \centering
\begin{tabular}{ l l r l}
	 exh 	&  Type	&  Reference & Formula\\ \toprule
     yes & \psynthetic{} & & $-$\\
 &  &  & $-$ \\
\lightrule
yes & \psmall{} &  & $-$\\
 &  &  & $-$\\
\lightrule
yes & \pextended{} &  & $-$\\
 &  &  & $-$\\
\strongrule

no 	&  \psynthetic{} 	& \analogy{} & $\hat{Y}_{G,psynth,3p} = \left( \hat{\bar{Z}}_{c,s_0,G}^{(1)}- \hat{\bar{Z}}_{c,s_1,G}^{(1)}\right) \hat{\alpha}_{c,2} + \hat{\bar{Z}}^t_{c,s_1,G}\hat{\beta}_{c,s_2} $\\
	   	&    	&    \analogy{} & $ \hat{V} = \hat{\alpha}_{c,s_2}^t \hat{\Sigma}_{\hat{\bar{Z}}_{c,s_0,G}^{(1)}} \hat{\alpha}_{c,s_2} + \frac{n_{s_2}}{n_{s_1}} \hat{\bar{Z}}^{(1)t}_{c,s_0,G} \hat{\Sigma}_{ \hat{\alpha}_{c,s_2}} \hat{\bar{Z}}^{(1)}_{c,s_0,G} + (1-\frac{n_{s_2}}{n_{s_1}})\hat{\bar{Z}}^{t}_{c,s_1,G} \hat{\Sigma}_{ \hat{\beta}_{c,s_2}} \hat{\bar{Z}}_{c,s_1,G} $\\
\lightrule
			
no 	&  \psmall{} 	& \analogy{} & $ \hat{Y}_{c,G,psmall,3p} = \hat{Y}_{G,psynth,G,3p} + \mRc$\\
	    	&      	& \analogy{} & $ \hat{V} \approx \hat{V}\left(\hat{\tilde{Y}}_{c,G,psynth,3p}\right) + \vRc$\\
\lightrule

no 	&  \pextended{} 	& \cite[eq. 53]{Man13c.e} & $ \hat{\tilde{Y}}_{c,G,g3reg} = \left( \hat{\bar{\eZ}}_{c,s_0,G}^{(1)}- \hat{\bar{\eZ}}_{c,s_1,G}^{(1)}\right) \hat{\gamma}_{c,2} + \hat{\bar{\eZ}}^t_{c,s_1,G}\hat{\theta}_{c,2}$\\
        &    	&     \cite[eq. 55]{Man13c.e} & $\hat{V} = \hat{\gamma}_{c,s_2}^t \hat{\Sigma}_{\hat{\bar{\eZ}}_{c,s_0,G}^{(1)}} \hat{\gamma}_{c,s_2} + \frac{n_{s_2}}{n_{s_1}} \hat{\bar{\eZ}}^{(1)t}_{c,s_0,G} \hat{\Sigma}_{ \hat{\gamma}_{c,s_2}} \hat{\bar{\eZ}}^{(1)}_{c,s_0,G} + (1-\frac{n_{s_2}}{n_{s_1}})\hat{\bar{\eZ}}^{t}_{c,s_1,G} \hat{\Sigma}_{ \hat{\theta}_{c,s_2}} \hat{\bar{\eZ}}_{c,s_1,G} $\\
\strongrule
part 	&  \psynthetic{} 	& \analogy{} & $\hat{Y}_{c,G,synth,3p} = \left(
\bar{Z}_{G}^{(1)}- \hat{\bar{Z}}_{c,s_1,G}^{(1)}\right) \hat{\alpha}_{c,}2 + \hat{\bar{Z}}^t_{c,s_1,G}\hat{\beta}_{c,s_2} $\\
	   	&    	&    \analogy{} & $ \hat{V} = \frac{n_{s_2}}{n_{s_1}} \hat{\bar{Z}}^{(1)t}_{c,s_0,G} \hat{\Sigma}_{ \hat{\alpha}_{c,s_2}} \hat{\bar{Z}}^{(1)}_{c,s_0,G} + (1-\frac{n_{s_2}}{n_{s_1}})\hat{\bar{Z}}^{t}_{c,s_1,G} \hat{\Sigma}_{ \hat{\beta}_{c,s_2}} \hat{\bar{Z}}_{c,s_1,G} $\\
\lightrule
			
part 	&  \psmall{} 	& \analogy{} & $ \hat{Y}_{c,G,small,3p} = \hat{Y}_{c,G,synth,3p} + \mRc$\\
	    	&      	& \analogy{} & $ \hat{V} \approx \hat{V}\left(\hat{Y}_{c,G,synth,3p}\right) + \vRc$\\
\lightrule

part 	&  \pextended{} 	& \analogy{} & $\hat{\tilde{Y}}_{c,G,ext
synth,3p} = \left( \bar{\eZ}_{G}^{(1)}- \hat{\bar{\eZ}}_{c,s_1,G}^{(1)}\right) \hat{\gamma}_{c,2} + \hat{\bar{\eZ}}^t_{c,s_1,G}\hat{\theta}_{c,2} $\\
	   	&    	&    \analogy{} & $ \hat{V} = \frac{n_{s_2}}{n_{s_1}} \hat{\bar{\eZ}}^{(1)t}_{c,s_0,G} \hat{\Sigma}_{ \hat{\gamma}_{c,s_2}} \hat{\bar{\eZ}}^{(1)}_{c,s_0,G} + (1-\frac{n_{s_2}}{n_{s_1}})\hat{\bar{\eZ}}^{t}_{c,s_1,G} \hat{\Sigma}_{ \hat{\theta}_{c,s_2}} \hat{\bar{\eZ}}_{c,s_1,G}$\\

\end{tabular}
\caption{Predictors for clustered three-phase sampling, 
    \emph{exh} denotes exhaustiveness of auxiliary information (yes/no/part, the
    latter meaning partially exhaustive auxiliary information),
    \emph{Type} denotes the area estimator (\psynthetic{} for synthetic, \psmall{}
    for small and \pextended{} for extended synthetic. \emph{Reference} gives the
    refenerce where found, else I derived them by analogy. \label{tab:clustered3}
}

\end{table}

