Independence tests for continuous random variables based on the longest increasing subsequence

dc.creatorGarcia, JE
dc.creatorGonzalez-Lopez, VA
dc.date2014
dc.dateMAY
dc.date2014-07-30T14:33:14Z
dc.date2015-11-26T17:40:08Z
dc.date2014-07-30T14:33:14Z
dc.date2015-11-26T17:40:08Z
dc.date.accessioned2018-03-29T00:21:47Z
dc.date.available2018-03-29T00:21:47Z
dc.identifierJournal Of Multivariate Analysis. Elsevier Inc, v. 127, n. 126, n. 146, 2014.
dc.identifier0047-259X
dc.identifierWOS:000334819700009
dc.identifier10.1016/j.jmva.2014.02.010
dc.identifierhttp://www.repositorio.unicamp.br/jspui/handle/REPOSIP/60053
dc.identifierhttp://repositorio.unicamp.br/jspui/handle/REPOSIP/60053
dc.identifier.urihttp://repositorioslatinoamericanos.uchile.cl/handle/2250/1286642
dc.descriptionFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.descriptionWe propose a new class of nonparametric tests for the supposition of independence between two continuous random variables X and Y. Given a size n sample, let pi be the permutation which maps the ranks of the X observations on the ranks of the Y observations. We identify the independence assumption of the null hypothesis with the uniform distribution on the permutation space. A test based on the size of the longest increasing subsequence of pi (L-n) is defined. The exact distribution of 1,5 is computed from Schensted's theorem (Schensted, 1961). The asymptotic distribution of L-n was obtained by Bail et al. (1999). As the statistic L-n is discrete, there is a small set of possible significance levels. To solve this problem we define the JL(n) statistic which is a jackknife version of L-n as well as the corresponding hypothesis test. A third test is defined based on the JLM(n) statistic which is a jackknife version of the longest monotonic subsequence of pi. On a simulation study we apply our tests to diverse dependence situations with null or very small correlations where the independence hypothesis is difficult to reject. We show that L-n, JL(n) and JLM(n) tests have very good performance on that kind of situations. We illustrate the use of those tests on two real data examples with small sample size. (C) 2014 Elsevier Inc. All rights reserved.
dc.description127
dc.description126
dc.description146
dc.descriptionUSP project "Mathematics, computation, language and the brain"
dc.descriptionFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.descriptionS. Paulo Research Foundation
dc.descriptionFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.descriptionFAPESP [2012/06078-9]
dc.descriptionFAPESP [2013/07699-0]
dc.languageen
dc.publisherElsevier Inc
dc.publisherSan Diego
dc.publisherEUA
dc.relationJournal Of Multivariate Analysis
dc.relationJ. Multivar. Anal.
dc.rightsfechado
dc.rightshttp://www.elsevier.com/about/open-access/open-access-policies/article-posting-policy
dc.sourceWeb of Science
dc.subjectLongest increasing subsequence
dc.subjectTest for independence
dc.subjectCopula
dc.titleIndependence tests for continuous random variables based on the longest increasing subsequence
dc.typeArtículos de revistas


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