Improved Point Estimation for the Rayleigh Regression Model
This work addresses bias issues in SAR image modeling for remote sensing applications, but it is incremental as it applies existing bias correction methods to a specific model.
The authors tackled bias in maximum likelihood estimators for the Rayleigh regression model used in synthetic aperture radar (SAR) image analysis, particularly for small pixel windows, by introducing bias-adjusted estimators based on Cox and Snell's method, Firth's scheme, and parametric bootstrap, resulting in nearly unbiased estimates and accurate modeling as shown in numerical experiments.
The Rayleigh regression model was recently proposed for modeling amplitude values of synthetic aperture radar (SAR) image pixels. However, inferences from such model are based on the maximum likelihood estimators, which can be biased for small signal lengths. The Rayleigh regression model for SAR images often takes into account small pixel windows, which may lead to inaccurate results. In this letter, we introduce bias-adjusted estimators tailored for the Rayleigh regression model based on: (i) the Cox and Snell's method; (ii) the Firth's scheme; and (iii) the parametric bootstrap method. We present numerical experiments considering synthetic and actual SAR data sets. The bias-adjusted estimators yield nearly unbiased estimates and accurate modeling results.