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

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  • Barone, P.

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 α-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 is proposed whose asymptotic relative efficiency w.r. to the van der Waerden type test when applied to the new sample is larger than one.

Suggested Citation

  • Barone, P., 2016. "Bivariate one-sample optimal location test for spherical stable densities by Pade’ methods," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 189-199.
    • Handle: RePEc:eee:jmvana:v:144:y:2016:i:c:p:189-199
    DOI: 10.1016/j.jmva.2015.11.008
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    References listed on IDEAS

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    1. Barone, P., 2013. "On the condensed density of the zeros of the Cauchy transform of a complex atomic random measure with Gaussian moments," Statistics & Probability Letters, Elsevier, vol. 83(11), pages 2569-2576.
    2. Barone, Piero, 2012. "On the condensed density of the generalized eigenvalues of pencils of Gaussian random matrices and applications," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 160-173.
    3. Hannu Oja, 1999. "Affine Invariant Multivariate Sign and Rank Tests and Corresponding Estimates: a Review," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(3), pages 319-343, September.
    4. John Nolan, 2013. "Multivariate elliptically contoured stable distributions: theory and estimation," Computational Statistics, Springer, vol. 28(5), pages 2067-2089, October.
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