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2012 Testing the finiteness of the support of a distribution: a statistical look at Tsirelson's equation
Sylvain Delattre, Mathieu Rosenbaum
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Electron. Commun. Probab. 17: 1-7 (2012). DOI: 10.1214/ECP.v17-1834

Abstract

We consider the following statistical problem: based on an i.i.d. sample of size $n$ of integer valued random variables with common law $\mu$, is it possible to test whether or not the support of $\mu$ is finite as $n$ goes to infinity? This question is in particular connected to a simple case of Tsirelson's equation, for which it is natural to distinguish between two main configurations, the first one leading only to laws with finite support, and the second one including laws with infinite support. We show that it is in fact not possible to discriminate between the two situations, even using a very weak notion of statistical test.

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Sylvain Delattre. Mathieu Rosenbaum. "Testing the finiteness of the support of a distribution: a statistical look at Tsirelson's equation." Electron. Commun. Probab. 17 1 - 7, 2012. https://doi.org/10.1214/ECP.v17-1834

Information

Accepted: 7 July 2012; Published: 2012
First available in Project Euclid: 7 June 2016

zbMATH: 1284.62127
MathSciNet: MR2955490
Digital Object Identifier: 10.1214/ECP.v17-1834

Subjects:
Primary: 62F03
Secondary: 62F05

Keywords: Hypothesis testing , Tsirelson's equation

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