Dealing with monotone likelihood in a model for speckled data

• Published in: Computational statistics & data analysis Vol. 55; no. 3; pp. 1394 - 1409
• Main Authors: Pianto, Donald M., Cribari-Neto, Francisco
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.03.2011; Elsevier
• Series: Computational Statistics & Data Analysis
• Subjects: [formula omitted] distribution; Bootstrap; Distribution theory; Estimates; Estimators; Exact sciences and technology; General topics; Mathematical analysis; Mathematical models; Mathematics; Monotone likelihood; Monte Carlo methods; Multivariate analysis; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in probability and statistics; Probability and statistics; Probability theory and stochastic processes; Roughness; Sciences and techniques of general use; Speckle; Speckle distribution Monotone likelihood Bootstrap; Statistical methods; Statistics; Synthetic aperture radar; Speckle; Bootstrap; Monotone likelihood; G A 0 distribution; Statistical distribution; Non parametric estimation; Multivariate analysis; Stochastic method; distribution; Implementation; Distribution function; Jackknife method; Approximation theory; Likelihood function; Monotonic function; Monte Carlo method; Discriminant analysis; Data analysis; Prior distribution; Statistical moment; g; Statistical estimation; Numerical analysis; Statistical computation; Maximum likelihood; Resampling method
• ISSN: 0167-9473; 1872-7352
• DOI: 10.1016/j.csda.2010.09.029

In this paper we study maximum likelihood estimation (MLE) of the roughness parameter of the G A 0 distribution for speckled imagery ( Frery et al., 1997). We discover that when a certain criterion is satisfied by the sample moments, the likelihood function is monotone and MLE estimates are infinite, implying an extremely homogeneous region. We implement three corrected estimators in an attempt to obtain finite parameter estimates. Two of the estimators are taken from the literature on monotone likelihood ( Firth, 1993; Jeffreys, 1946) and one, based on resampling, is proposed by the authors. We perform Monte Carlo experiments to compare the three estimators. We find the estimator based on the Jeffreys prior to be the worst. The choice between Firth’s estimator and the Bootstrap estimator depends on the value of the number of looks (which is given before estimation) and the specific needs of the user. We also apply the estimators to real data obtained from synthetic aperture radar (SAR). These results corroborate the Monte Carlo findings. Further clarification of the choice between the Firth and Bootstrap estimators will be obtained through future studies of the classification properties of these estimators.