Bivariate Fay-Herriot Model for Enhanced Small Area Estimation of Growing Stock Volume

Forest inventories are indispensable for the efficient and sustainable management of forest ecosystems. While design-based direct estimates are generally reliable for large subpopulations, their effectiveness diminishes for smaller geographic areas characterized by limited sample sizes, such as forest stands or management units. To address this challenge, the present study introduces an advanced bivariate area-level Fay-Herriot model. This model leverages auxiliary data from satellite-derived height metrics and historical censuses to concurrently estimate the growing stock volume for the years 2008 and 2018, with a specific focus on enhancing the precision of the 2018 estimates. The model incorporates both sampling errors and random area effects, and it capitalizes on the correlation between the response variables. This extends the basic univariate linear-mixed Fay-Herriot model into a more comprehensive estimation framework. Data preparation procedures included cluster analysis for grouping forest management units, correlation analysis, and outlier detection as preliminary preprocessing steps. Conducted in the University Forest of Pertouli in central Greece, our proposed model was benchmarked against both univariate Fay-Herriot models and direct estimators. The results indicate that our model yields more reliable estimates, as evidenced by improved mean square errors, coefficients of variation, and bias metrics. This research contributes to small area estimation methodology, particularly in forest inventory, thereby elevating the accuracy and sustainability of forest management practices.