On a characterization theorem of symmetry about a point

Let X1,…,Xn be i.i.d. copies of random variable X where 0<E|X|<∞ and let X̄=1n∑i=1nXi. One can show that X1−X̄,…,Xn−X̄ are exchangeable, and as a result identically distributed, but not independent. We use this result to prove that for n≥3, X is symmetric about a point if and only if X1−X̄ is symmetric. The theorem is applied for testing symmetry about an unknown point.

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Year of publication:	2013
Authors:	Behboodian, Javad ; Modarres, Reza
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 83.2013, 9, p. 2057-2059
Publisher:	Elsevier
Subject:	Exchangeability \| Symmetric distribution \| Law of large numbers

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10011039798