Robust scale estimation for the generalized Gaussian probability density function

Abstract

This article proposes a robust way to estimate the scale parameter of a generalised centered Gaussian mixture. The principle relies on the association of samples of this mixture to generate samples of a new variable that shows relevant distribution properties to estimate the unknown parameter. In fact, the distribution of this new variable shows a maximum that is linked to this scale parameter. Using nonparametric modelling of the distribution and the MeanShift procedure, the relevant peak is identified and an estimate is computed. The whole procedure is fully automatic and does not require any prior settings. It is applied to regression problems, and digital data processing.