Bias-corrected estimation for GI0 regression with applications

Synthetic aperture radar (SAR) systems are highly efficient tools for addressing remote sensing challenges. They offer several advantages, such as operating independently of atmospheric conditions and producing high spatial resolution images. However, SAR images are often contaminated by a type of interference called speckle noise, which complicates their analysis and processing. Therefore, proposing statistical methods, such as regression models, that account for speckle behavior is an important step for users of SAR systems. In the work [ISPRS J. Photogramm. Remote Sens., 213, 1-13, 2024], the G(I)(0) regression model (short for RG(I)(0 )was proposed as an interpretable tool to relate SAR intensity features to other physical properties. The authors employed maximum likelihood estimators (MLEs), known for their good asymptotic properties but prone to considerable bias in small and medium sample sizes. In this paper, we propose a matrix expression for the second-order bias of MLEs for RG(I)(0) parameters, based on the Cox and Snell method. This proposal is justified by the necessity of using small and moderate windows when processing SAR images, such as for classification and filtering purposes. We compare bias-corrected MLEs with their counterparts using both Monte Carlo experiments and an application to SAR data from a Brazilian region. Numerical evidence demonstrates the effectiveness of our proposal.