Improved likelihood inference for the roughness parameter of the GA0 distribution

This paper presents adjusted profile likelihoods for alpha, the roughness parameter of the G(A)(0) (alpha, gamma, L) distribution. This distribution has been widely used in the modeling, processing and analysis of data corrupted by speckle noise, e.g., synthetic aperture radar images. Specifically, we consider the following modified profile likelihoods: (i) the one proposed by Cox and Reid, and (ii) approximations to adjusted profile likelihood proposed by Barndorff-Nielsen, namely the approximations proposed by Severini and one based on results by Fraser, Reid and Wu. We focus on point estimation and on signalized likelihood ratio tests, the parameter of interest being the roughness parameter that indexes the distribution. As far as point estimation is concerned, the numerical evidence presented in the paper favors the Cox and Reid adjustment, and in what concerns signalized likelihood ratio tests, the results favor the approximation to Barndorff-Nielsen's adjustment based on the results by Fraser, Reid and Wu. An application to real synthetic aperture radar imagery is presented and discussed. Copyright (C) 2007 John Wiley & Sons, Ltd.