A note on the coefficients of elliptical random variables

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Abstract

It is well-known that the sum of elliptical random variables with constant coefficients is also an elliptical random variable. In this note, we prove that the coefficients can also be random variables, such that the sum of elliptical random variables with random coefficients on a circle is also elliptically distributed. We then examine statistical implications by considering the projection pursuit with the underlying random variables.

Original languageEnglish
Pages (from-to)153-155
Number of pages3
JournalStatistics and Probability Letters
Volume152
DOIs
StatePublished - 1 Sep 2019

Keywords

  • Elliptical distributions
  • Projection pursuit
  • Stopping rules
  • Weighted-sum
  • Wiener process

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