Random Permutations, Non-Decreasing Subsequences and Statistical Independence
Department of Statistics, University of Campinas, Sérgio Buarque de Holanda, 651, Campinas 13083-859, São Paulo, Brazil
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Symmetry 2020, 12(9), 1415; https://doi.org/10.3390/sym12091415
Received: 1 August 2020 / Revised: 14 August 2020 / Accepted: 21 August 2020 / Published: 26 August 2020
(This article belongs to the Special Issue Selected Papers from the 17th international Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2019))
In this paper, we show how the longest non-decreasing subsequence, identified in the graph of the paired marginal ranks of the observations, allows the construction of a statistic for the development of an independence test in bivariate vectors. The test works in the case of discrete and continuous data. Since the present procedure does not require the continuity of the variables, it expands the proposal introduced in Independence tests for continuous random variables based on the longest increasing subsequence (2014). We show the efficiency of the procedure in detecting dependence in real cases and through simulations.
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Keywords:
symmetric group; permutations; hypothesis tests
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MDPI and ACS Style
García, J.E.; González-López, V.A. Random Permutations, Non-Decreasing Subsequences and Statistical Independence. Symmetry 2020, 12, 1415. https://doi.org/10.3390/sym12091415
AMA Style
García JE, González-López VA. Random Permutations, Non-Decreasing Subsequences and Statistical Independence. Symmetry. 2020; 12(9):1415. https://doi.org/10.3390/sym12091415
Chicago/Turabian StyleGarcía, Jesús E.; González-López, Verónica A. 2020. "Random Permutations, Non-Decreasing Subsequences and Statistical Independence" Symmetry 12, no. 9: 1415. https://doi.org/10.3390/sym12091415
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