Estimation and tests under L-moment condition models and applications to radar detection

Since their introduction by Hosking in 1990, L-moments methods has become popular in applications dealing with extreme phenomenon whose underlying distribution is heavy-tailed. They constitute a robust alternative to traditional moment in the estimation of the "form" of the distribution because they effectively captures this type of information. It is therefore natural to generalize L-moment method as the generalized moment methods (GMM) for the moments. We introduce an equivalent point of view for the M-estimators based on the minimization of a divergence with moment constraints. This point of view relies on the minimization of a specific transformation energy instead of the minimization of a distance between two measures of probability. Many definitions of this transformation energy could be taken, we choose one that brings a linear minimization problem for L-moment constraints. Applications of such estimators to the radar detection of small targets in heterogeneous clutter will be presented. These clutters are modelized by a heavy-tail distribution traditionnally hard to estimate without strong hypothesis.