Bivariate one-sample optimal location test for spherical stable densities by Pade' methods

Abstract

Complex signal detection in additive noise can be performed by a one-sample bivariate location test. Spherical symmetry is assumed for the noise density as well as closedness with respect to linear transformation. Therefore the noise is assumed to have spherical distribution with $\alpha-$stable radial density. In order to cope with this difficult setting the original sample is transformed by Pade' methods giving rise to a new sample with universality properties. The stability assumption is then reduced to the Gaussian one and it is proved that a known van der Waerden type test, with optimal properties, based on the new sample can be used. Furthermore a new test in the same class of optimal tests is proposed which is more powerful that the van der Waerden type one.