[Probabilidad-Estadistica-Seminario] Seminario de Probabilidad y Estadística -- Viernes 14 de diciembre

[Andrés Sosa]

Hola

Este *viernes 14 de diciembre a las 10:30 horas* en el salón de seminarios
del Centro de Matemática hablará  *Gordana Drasković* (Université
Paris-Sud) en el seminario de Probabilidad y Estadística.

El título de la charla es:  *New insights into the statistical properties
of M-estimators with application to signal detection and PolSAR image
denoising.*

Saludos
Andrés


*Resumen:In signal processing applications, the knowledge of scatter matrix
is of crucial importance. It arises in diverse applications such as
filtering, detection, estimation or classification. Generally, in most of
signal processing methods the data can be locally modelled by a
multivariate zero-mean circular Gaussian stochastic process, which is
completely determined by its covariance matrix. In that case, the classical
covariance matrix estimator is the sample covariance matrix (SCM) whose
behavior is perfectly known. Indeed, it follows the well-known Wishart
distribution. Nevertheless, the complex normality sometimes presents a poor
approximation of underlying physics. An alternative has been proposed by
introducing elliptical distributions, namely the Complex Elliptically
Symmetric distributions. In this context the SCM can perform very poorly
and M-estimators appear as very interesting candidates, mainly due to their
flexibility to the statistical model and their robustness to outliers
and/or missing data. However, the behavior of such estimators still remains
unclear and not well understood since they are described by fixed-point
equations that make their statistical analysis very difficult. To fill this
gap, the main contribution of this work is to prove that these estimators
distribution is more accurately described by a Wishart distribution than by
the classical asymptotic Gaussian approximation. These results can be of
great interest in a wide range of signal processing problems such as
adaptive detection problems, polarimetric SAR images restoration, target
detection, clustering etc.*
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