Temporal-Like Bivariate Fay-Herriot Model: Leveraging Past Responses and Advanced Preprocessing for Enhanced Small Area Estimation of Growing Stock Volume

Abstract

AbstractForest inventories are crucial for effective ecosystem management but often lack precision for smaller geographical units due to limited sample sizes. This study introduces an enhanced temporal-like bivariate Fay-Herriot model, improving upon its univariate counterpart. The model incorporates field data and auxiliary data, including canopy height metrics from WorldView stereo-imagery and past census data, sourced from the University Forest of Pertouli in Central Greece. The model aims to estimate the growing stock volume for 2008 and 2018, focusing on enhancing the precision of the 2018 estimates. The 2008 dependent variable is used as auxiliary information by the model for more reliable 2018 small area estimates. A novel preprocessing pipeline is also introduced, which includes outlier identification, cluster analysis, and variance smoothing. Compared to direct estimates and the standard univariate Fay-Herriot model, our bivariate approach shows a percentage variance reduction of 96.58% and 13.52%, respectively. The methodology not only offers more reliable estimates with reduced variance and bias but also contributes to more accurate decision-making for sustainable forest management.