Improved likelihood inference for the roughness parameter of the GA0 distribution

Silva, Michel Ferreira Da; Cribari‐Neto, Francisco; Frery, Alejandro C.

doi:10.1002/env.881

Cited by 24 publications

(16 citation statements)

References 23 publications

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“…3) spatiotemporal contextual classification [8], [9]; 4) Hotelling-Lawley and likelihood ratio tests [10]- [19] and robust tests [20]; 5) combination of image rationing and the generalized minimum-error method [21]; 6) detection algorithms based on Lagrange optimization [22]; 7) information-theoretic measures for change detection [9], [23]- [30]; 8) change detection with postclassification [31]. This paper advances points 4) and 7) above.…”

mentioning

confidence: 73%

Detecting Changes in Fully Polarimetric SAR Imagery With Statistical Information Theory

Nascimento¹,

Frery²,

Cintra³

2021

Preprint

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© 1980-2012 IEEE. Images obtained from coherent illumination processes are contaminated with speckle. A prominent example of such imagery systems is the polarimetric synthetic aperture radar (PolSAR). For such a remote sensing tool, the speckle interference pattern appears in the form of a positive-definite Hermitian matrix, which requires specialized models and makes change detection a hard task. The scaled complex Wishart distribution is a widely used model for PolSAR images. Such a distribution is defined by two parameters: the number of looks and the complex covariance matrix. The last parameter contains all the necessary information to characterize the backscattered data, and thus, identifying changes in a sequence of images can be formulated as a problem of verifying whether the complex covariance matrices differ at two or more takes. This paper proposes a comparison between a classical change detection method based on the likelihood ratio and three statistical methods that depend on information-theoretic measures: the Kullback-Leibler (KL) distance and two entropies. The performance of these four tests was quantified in terms of their sample test powers and sizes using simulated data. The tests are then applied to actual PolSAR data. The results provide evidence that tests based on entropies may outperform those based on the KL distance and likelihood ratio statistics.

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confidence: 73%

Detecting Changes in Fully Polarimetric SAR Imagery With Statistical Information Theory

Nascimento¹,

Frery²,

Cintra³

2021

Preprint

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“…In [15] Barndorff-Nielsen introduced an improved ML estimation based on the modified profile likelihood. This method was previously employed in [16]- [18]. Below we furnish a brief outline of the technique.…”

Section: Barndorff-nielsen ML Estimatormentioning

confidence: 99%

Bias Correction and Modified Profile Likelihood Under the Wishart Complex Distribution

Nascimento

Frery

Cintra

2014

IEEE Trans. Geosci. Remote Sensing

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Abstract-This paper proposes improved methods for the maximum likelihood (ML) estimation of the equivalent number of looks L. This parameter has a meaningful interpretation in the context of polarimetric synthetic aperture radar (PolSAR) images. Due to the presence of coherent illumination in their processing, PolSAR systems generate images which present a granular noise called speckle. As a potential solution for reducing such interference, the parameter L controls the signal-noise ratio. Thus, the proposal of efficient estimation methodologies for L has been sought. To that end, we consider firstly that a PolSAR image is well described by the scaled complex Wishart distribution. In recent years, Anfinsen et al. derived and analyzed estimation methods based on the ML and on trace statistical moments for obtaining the parameter L of the unscaled version of such probability law. This paper generalizes that approach. We present the second-order bias expression proposed by Cox and Snell for the ML estimator of this parameter. Moreover, the formula of the profile likelihood modified by Barndorff-Nielsen in terms of L is discussed. Such derivations yield two new ML estimators for the parameter L, which are compared to the estimators proposed by Anfinsen et al.. The performance of these estimators is assessed by means of Monte Carlo experiments, adopting three statistical measures as comparison criterion: the mean square error, the bias, and the coefficient of variation. Equivalently to the simulation study, an application to actual PolSAR data concludes that the proposed estimators outperform all the others in homogeneous scenarios.

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“…A number of recent papers have successfully obtained analytic expressions for which are valid to O(n -1 ), based on the work of Cox and Snell (1968), and Cordeiro and Klein (1994). Some examples include: Cordeiro and McCullagh (1991), Cordeiro et al (1996), Cribari-Neto and Vasconcellos (2002), Cordeiro and Vasconcellos (1997), Silva et al (2008), Giles (2012), Giles et al (2013Giles et al ( , 2016, Schwartz et al (2013), Schwartz and Giles (2016), and Godwin (2016). A useful overview of this topic is provided by Cordeiro and Cribari-Neto (2014).…”

Section: Introductionmentioning

confidence: 99%

Analytic bias correction for maximum likelihood estimators when the bias function is non-constant

Godwin

Giles

2017

Communications in Statistics - Simulation and Computation

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Recently, many papers have obtained analytic expressions for the biases of various maximum likelihood estimators, despite their lack of closed-form solution. These bias expressions have provided an attractive alternative to the bootstrap. Unless the bias function is "flat," however, the expressions are being evaluated at the wrong point(s). We propose an "improved" analytic bias adjusted estimator, in which the bias expression is evaluated at a more appropriate point (at the bias adjusted estimator itself). Simulations illustrate that the improved analytic bias adjusted estimator can eliminate significantly more bias than the simple estimator which has been well established in the literature.

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Improved likelihood inference for the roughness parameter of the GA0 distribution

Cited by 24 publications

References 23 publications

Detecting Changes in Fully Polarimetric SAR Imagery With Statistical Information Theory

Detecting Changes in Fully Polarimetric SAR Imagery With Statistical Information Theory

Bias Correction and Modified Profile Likelihood Under the Wishart Complex Distribution

Analytic bias correction for maximum likelihood estimators when the bias function is non-constant

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