Alleviating small sample problem in continuous forest monitoring with remote sensing-assisted Copulas

Abstract

With model-assisted (MA) estimation, remote sensing (RS) has provided auxiliary modeling data to enhance precision in estimators of forest parameters for continuous forest monitoring as mandated by various official reporting instruments. However, model-assisted estimation is largely reliant on a sample resulting from costly field surveys to meet the precision standard mandated by these instruments. While a large sample is more likely to represent the population in question and ensure meeting the prescribed precision, it is crucial to reduce costs by finding a balance between precision and sample size. Consequently, this study aims to (1) develop and demonstrate estimation using Copulas modeling; (2) propose a sample size optimization procedure for MA estimators in the context of continuous forest monitoring; and (3) compare survey precisions of the estimators using Copulas and Weighted Least Squares regression (WLS) as a function of sample sizes. Four main conclusions are relevant: for both Burkina Faso (BF) and Genhe (GH) study area, (1) Copulas outperforms WLS in modeling and prediction, both in terms of mean values and maximum/minimum values; (2) Copulas consistently demonstrates superior performance and precision across varying sample sizes compared to the WLS with MA estimators; (3) a straightforward sample size optimization approach reveals that variance estimates of Copulas remain lower than those of WLS as the sample size decreases in monitoring surveys; (4) Copulas requires about 20% smaller sample size than WLS does when achieving a specified precision, suggesting enhanced efficiency. Overall, Copulas appears promising to satisfy the precision, cost-efficiency, and flexibility requirements of monitoring surveys, particularly in situations involving small sample sizes.