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High-dimensional star-shaped distributions

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  • Wolf-Dieter Richter

    (University of Rostock, Institute of Mathematics)

Abstract

Stochastic representations of star-shaped distributed random vectors having heavy or light tail density generating function g are studied for increasing dimensions along with corresponding geometric measure representations. Intervals are considered where star radius variables take values with high probability, and the derivation of values of distribution functions of g-robust statistics is proved to be based upon considering random events whose probability is asymptotically negligible if the dimension of the sample vector is approaching infinity. Moreover, a principal component representation of p-generalized elliptically contoured p-generalized Gaussian distributions is discussed.

Suggested Citation

  • Wolf-Dieter Richter, 2019. "High-dimensional star-shaped distributions," Journal of Statistical Distributions and Applications, Springer, vol. 6(1), pages 1-12, December.
    • Handle: RePEc:spr:jstada:v:6:y:2019:i:1:d:10.1186_s40488-019-0096-0
    DOI: 10.1186/s40488-019-0096-0
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    References listed on IDEAS

    as
    1. Balkema, A.A. & Embrechts, P. & Nolde, N., 2010. "Meta densities and the shape of their sample clouds," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1738-1754, August.
    2. Wolf-Dieter Richter & Kay Schicker, 2017. "Polyhedral Star-Shaped Distributions," Journal of Probability and Statistics, Hindawi, vol. 2017, pages 1-23, February.
    3. Wolf-Dieter Richter, 2016. "Exact inference on scaling parameters in norm and antinorm contoured sample distributions," Journal of Statistical Distributions and Applications, Springer, vol. 3(1), pages 1-16, December.
    4. Henschel, V. & Richter, W. -D., 2002. "Geometric Generalization of the Exponential Law," Journal of Multivariate Analysis, Elsevier, vol. 81(2), pages 189-204, May.
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    Cited by:

    1. Liebscher Eckhard & Richter Wolf-Dieter, 2020. "Modelling with star-shaped distributions," Dependence Modeling, De Gruyter, vol. 8(1), pages 45-69, January.
    2. Liebscher Eckhard & Richter Wolf-Dieter, 2020. "Modelling with star-shaped distributions," Dependence Modeling, De Gruyter, vol. 8(1), pages 45-69, January.

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