High-dimensional star-shaped distributions

Wolf-Dieter Richter ()
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Wolf-Dieter Richter: University of Rostock, Institute of Mathematics

Journal of Statistical Distributions and Applications, 2019, vol. 6, issue 1, 1-12

Abstract: 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.

Keywords: Increasing dimension; Star-shaped distribution; Star radius distribution; Star-uniform distribution; p-generalized elliptically contoured distribution; Principal component representation; g-robust statistic; Indeterminate form (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1186/s40488-019-0096-0

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