Strongly consistent nonparametric tests of conditional independence

Statistics and Probability Letters

Volumn 82, Issue 6, 2012, Pages 1145-1150

  Györfi, László ^a   Walk, Harro ^b  

^a BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS   (Hungary)

^b UNIVERSITY OF STUTTGART   (Germany)

Author keywords

Conditional independence; Distribution free strong consistency; Nonparametric test; Partition

Indexed keywords

EID: 84859024018     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spl.2012.02.023     Document Type: Article

References (30)

1. Bakirov N., Rizzo M., Székely G. A multivariate nonparametric test of independence. J. Multivariate Anal. 2006, 97:1742-1756.
2. Barron A.R., Györfi L., van der Meulen E.C. Distribution estimation consistent in total variation and in two types of information divergence. IEEE Trans. Information Theory 1992, 38:1437-1454.
3. Beirlant J., Devroye L., Györfi L., Vajda I. Large deviations of divergence measures on partitions. J. Statist. Plann. Inference 2001, 93:1-16.
4. Beran R., Bilodeau M., Lafaye de Micheaux P. Nonparametric tests of independence between random vectors. J. Multivariate Anal. 2007, 98:1805-1824.
5. 1-test statistic of homogeneity. IEEE Trans. Information Theory 2005, 51:3965-3973.
6. Blum J.R., Kiefer J., Rosenblatt M. Distribution free tests of independence based on the sample distribution function. Ann. Math. Statist. 1961, 32:485-498.
7. Cotterill D.S., Csörgo M. On the limiting distribution of and critical values for the Hoeffding, Blum, Kiefer, Rosenblatt independence criterion. Statist. Decisions 1985, 3:1-48.
8. Csörgo S. Testing for independence by the empirical characteristic function. J. Multivariate Anal. 1985, 16:290-299.
9. Dauxois J., Nkiet G.M. Nonlinear canonical analysis and independence tests. Ann. Statist. 1998, 26:1254-1278.
10. de Campos L.M. A scoring function for learning Bayesian networks based on mutual information and conditional independence tests. J. Mach. Learning Res. 2006, 7:2149-2187.
11. Dembo A., Peres Y. A topological criterion for hypothesis testing. Ann. Statist. 1994, 22:106-117.
12. Dette H., Neumeyer N. A note on a specification test of independence. Metrika 2000, 51:133-144.
13. Devroye L., Lugosi G. Almost sure classification of densities. J. Nonpar. Statist. 2002, 14:675-698.
14. De Wet T. Cramér-von Mises tests for independence. J. Multivariate Anal. 1980, 10:38-50.
15. Feuerverger A. A consistent test for bivariate dependence. Internat. Statist. Rev. 1993, 61:419-433.
16. Fukumizu K., Bach F., Gretton A. Statistical consistency of kernel canonical correlation analysis. J. Mach. Learning Res. 2007, 8:361-383.
17. Genest C., Quessy J.F., Remillard B. Asymptotic local efficiency of Cramér-von Mises tests for multivariate independence. Ann. Statist. 2007, 35:166-191.
18. Gieser P., Randles R. A nonparametric test of independence between two vectors. J. Amer. Statist. Assoc. 1997, 92:561-567.
19. Gretton A., Györfi L. Consistent nonparametric tests of independence. J. Mach. Learning Res. 2010, 11:1391-1423.
20. Gretton A., Herbrich R., Smola A., Bousquet O., Schölkopf B. Kernel methods for measuring independence. J. Mach. Learning Res. 2005, 6:2075-2129.
21. Györfi L., Kohler M., Krzyzak A., Walk H. A Distribution-Free Theory of Nonparametric Regression 2002, Springer, New York.
22. Györfi L., van der Meulen E.C. A consistent goodness of fit test based on the total variation distance. Nonparametric Functional Estimation and Related Topics 1990, 631-645. Kluwer, Dordrecht. G. Roussas (Ed.).
23. Hoeffding W. A nonparametric test for independence. Ann. Math. Statist. 1948, 19:546-557.
24. Kankainen, A., 1995. Consistent Testing of Total Independence Based on the Empirical Characteristic Function. Ph.D. Thesis, University of Jyväskylä.
25. Kullback S. Information Theory and Statistics 1968, Dover Publications, London.
26. Linton O., Gozalo P. Conditional independence restrictions: testing and estimation. Cowles Foundation Discussion Papers 1996, 1140:47 pp.
27. Rosenblatt M. A quadratic measure of deviation of two-dimensional density estimates and a test of independence. Ann. Statist. 1975, 3:1-14.
28. Song K. Testing conditional independence via Rosenblatt transforms. Ann. Statist. 2009, 37:4011-4045.
29. Su L., White H. A nonparametric Hellinger metric test for conditional independence. Econometric Theory 2008, 24:829-864.
30. Su L., White H. A consistent characteristic function-based test for conditional independence. J. Econometrics 2008, 143:123-142.