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Testing the finiteness of the support of a distribution: a statistical look at Tsirelson's equation


 
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1. Title Title of document Testing the finiteness of the support of a distribution: a statistical look at Tsirelson's equation
 
2. Creator Author's name, affiliation, country Sylvain Delattre; Université Paris Diderot (Paris 7); France
 
2. Creator Author's name, affiliation, country Mathieu Rosenbaum; Université Pierre et Marie Curie (Paris 6); France
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Hypothesis testing; Tsirelson's equation
 
3. Subject Subject classification 62F03; 62F05
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2012-07-07
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1834
 
10. Identifier Digital Object Identifier 10.1214/ECP.v17-1834
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 17
 
12. Language English=en en
 
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