Abstract
In the presence of weak overall correlation, it may be useful to investigate if the correlation is significantly and substantially more pronounced over a subpopulation. Two different testing procedures are compared. Both are based on the rankings of the values of two variables from a data set with a large number n of observations. The first maintains its level against Gaussian copulas; the second adapts to general alternatives in the sense that the number of parameters used in the test grows with n. An analysis of wine quality illustrates how the methods detect heterogeneity of association between chemical properties of the wine, which are attributable to a mix of different cultivars.
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References
Aeberhard, S., Coomans, D., de Vel, O.: Improvements to the classification performance of RDA. J. Chemometr. 7 (2), 99–115 (1993)
Diaconis, P., Graham, R.L.: Spearman’s footrule as a measure of disarray. J. R. Stat. Soc. Ser. B - Stat. Methodol. 39, 262–268 (1977)
Diaconis, P., Ram, A.: Analysis of systematic scan metropolis algorithms using Iwahori-Hecke algebra techniques. Mich. Math. J. 48, 157–190 (2000)
Fermanian, J.D., Radulovic, D., Wegkamp, M.: Weak convergence of empirical copula processes. Bernoulli 10, 847–860 (2004)
Fligner, M.A., Verducci, J.S.: Distance based ranking models. Journal of the Royal Statistical Society B, 48, 359–369 (1986)
Frank, M.J.: On the simultaneous associativity of F(x, y) and x + y − F(x, y). Aequationes Math. 19, 194–226 (1979)
Genest, C.: Frank’s family of bivariate distributions. Biometrika 74 (3), 549–555 (1987)
Genest, C., MacKay, J.: The joy of copulas: bivariate distributions with uniform marginals. Am. Stat. 40, 280–283 (1986)
Genest, C., Nešlehová, J.: On tests of radial symmetry for bivariate copulas. Stat. Pap. 55, 1107–1119 (2014)
Katz, G.: How much do we know about HDL cholesterol? Clin. Correlat. (2014) (http://www.clinicalcorrelations.org/?p=7298)
Lehmann, E.L., Romano, J.P.: Testing Statistical Hypotheses, 3rd edn. Springer, New York (2006).
Mallows, C.: Non-Null Ranking Models. Biometrika, 44 (1), 114–130 (1957)
Nelsen, R.B.: An Introduction to Copulas, 2nd edn. Springer, New York (2006)
Sampath, S., Verducci, J.: Detecting the end of agreement between two long ranked lists. Stat. Anal. Data Min. 6 (6), 458–471 (2013)
Sampath, S., Caloiaro, A., Johnson, W., Verducci, J.: The top-K tau-path screen for monotone association in subpopulations. WIREs Comput. Stat. (2016). doi:10.1002/wics.1382
Sen, P.K., Salama, I.A., Quade, D.: Spearman’s footrule: asymptotics in applications. Chil. J. Stat. 2, 3–20 (2011)
Starr, S.: Thermodynamic limit for the Mallows model on S n . J. Math. Phys. 50, 195–208 (2009)
Voight, B.F., et al.: Plasma HDL cholesterol and risk of myocardial infarction: a Mendelian randomisation study. Lancet 380 (9841), 572–580 (2012)
Yu, L., Verducci, J., Blower, P.: The tau-path test for monotone association in an unspecified subpopulation: applications to chemogenomic data mining. Stat. Methodol. 8, 97–111 (2011)
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Bamattre, S., Hu, R., Verducci, J.S. (2017). Nonparametric Testing for Heterogeneous Correlation. In: Ahmed, S. (eds) Big and Complex Data Analysis. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-41573-4_12
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DOI: https://doi.org/10.1007/978-3-319-41573-4_12
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