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There is a growing demand for improving the measurement of forest resources, with more frequent updating and better information on environmental variables. We explore the cost efficiency of a stratified two-stage design using area sampling to estimate the forest plantation and native forest areas in southern Chile. Analytical expressions for the approximate mean square error of combined and separate ratio estimators are derived applying Taylor linearization. Under a unified framework, this procedure allows the evaluation of the precision of design and post-design estimators for unequal unit area sizes at both stages. Monte Carlo simulations were used to assess empirically the approximate analytical measures of the mean square error and the biases associated with the ratio estimators. Adopting proportional allocation among strata and clusters, the optimal allocation among the two stages is determined. A substantial improvement in sampling precision was achieved using the separate ratio estimator and the bias was found to be small. Post-stratification based on categorical information on growing zones also improved the precision of estimating the forest plantation area and a smaller extent the native forest area. The results of this paper support a wider adoption of sampling methods to estimate land use and land cover at regional or national levels.
