A note on the coefficients of elliptical random variables

Tomer Shushi

doi:10.1016/j.spl.2019.05.004

A note on the coefficients of elliptical random variables

Tomer Shushi

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	153-155
Number of pages	3
Journal	Statistics and Probability Letters
Volume	152
DOIs	https://doi.org/10.1016/j.spl.2019.05.004
State	Published - Sep 2019
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2019 Elsevier B.V.

Keywords

Elliptical distributions
Projection pursuit
Stopping rules
Weighted-sum
Wiener process

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1016/j.spl.2019.05.004

Cite this

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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.",

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AB - 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.

KW - Elliptical distributions

KW - Projection pursuit

KW - Stopping rules

KW - Weighted-sum

KW - Wiener process

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M3 - Article

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VL - 152

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EP - 155

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

ER -

A note on the coefficients of elliptical random variables

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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