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

Author(s)

Garcia, Jesus E. ^[1] ; Gonzalez-Lopez, V. A. ^[1]

Affiliation

^[1] Univ Estadual Campinas, Dept Stat, BR-13083859 Campinas, SP - Brazil

• Document type: Journal article
• Source: JOURNAL OF MULTIVARIATE ANALYSIS; v. 127, p. 126-146, MAY 2014.
• Web of Science Citations: 4

Abstract

We 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. (AU)

• FAPESP's process: 13/07699-0 - Research, Innovation and Dissemination Center for Neuromathematics - NeuroMat
• Grantee: Oswaldo Baffa Filho
• Support Opportunities: Research Grants - Research, Innovation and Dissemination Centers - RIDC
• FAPESP's process: 12/06078-9 - Portuguese in time and space: linguistic contact, grammars in competition and parametric change
• Grantee: Charlotte Marie Chambelland Galves
• Support Opportunities: Research Projects - Thematic Grants