A new approach to small area estimation: improving forest management unit estimates with advanced preprocessing in a multivariate Fay-Herriot model

Forest inventories are essential for informing sustainable forest management decisions, and small area estimation (SAE) techniques aim to enhance the precision of these inventories, particularly when sample sizes are limited. This study presents a novel approach to SAE by integrating trivariate empirical best linear unbiased prediction Fay-Herriot (FH) models with advanced preprocessing techniques. By employing multivariate Fay-Herriot (MFH) models, the methodology utilizes clustering analysis, variable selection, and outlier treatment to improve the precision of estimates for small areas. A comparative analysis with traditional univariate Fay-Herriot (UFH) models demonstrates that MFH outperforms UFH in estimating key forest attributes such as forest growing stock volume, basal area, and Lorey's mean tree Height, even in areas with limited sample sizes. The use of auxiliary variables derived from remote sensing data and past censuses proved critical, with remote sensing playing a dual role: aiding in clustering forest management units into larger small areas of interest and serving as covariates in the FH models. The results highlight the effectiveness of MFH1 (assuming independent and identically distributed random effects), which consistently produced estimates with <5% coefficient of variation, indicating high precision. Across all response variables, MFH1 led to reductions in standard errors compared to UFH, with median percentage gains in precision of 17.22% for volume, 13.91% for basal area, and 3.95% for mean height. Mean precision gains were even higher, at 18.27%, 16.51%, and 10.87%, respectively. This study advances SAE methodologies by providing a robust framework for accurately estimating critical forest attributes in challenging scenarios, including geolocation errors, limited sample sizes, and the smallest applicable small areas for area-level models. It highlights the contribution of the correlation between multiple response variables to improving the precision of estimates. The proposed methodology has significant implications for enhancing the accuracy of forest inventories and supporting informed forest management decisions.