Improved Point Estimation for the Rayleigh Regression Model

TL;DR

This paper introduces bias-adjusted estimators for the Rayleigh regression model used in SAR image analysis, improving inference accuracy for small sample sizes through three different bias correction methods.

Contribution

It proposes new bias-adjusted estimators for the Rayleigh regression model, enhancing inference accuracy in small sample scenarios compared to traditional maximum likelihood estimators.

Findings

Bias-adjusted estimators are nearly unbiased.

Improved modeling accuracy demonstrated with synthetic and real SAR data.

Methods outperform traditional estimators in small sample contexts.

Abstract

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.