Document Zbl 0486.62043

An asymptotic decomposition for multivariate distribution-free tests of independence. (English) Zbl 0486.62043

J. Multivariate Anal. 11, 102-113 (1981).

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MSC:

62G10	Nonparametric hypothesis testing
62E20	Asymptotic distribution theory in statistics
62H10	Multivariate distribution of statistics
62H15	Hypothesis testing in multivariate analysis
60E10	Characteristic functions; other transforms
60G15	Gaussian processes

Keywords:

asymptotic decomposition; tests of independence; limiting Gaussian process; Karhunen-Loeve expansions; rank statistics; empirical measures; Cramer-von Mises statistics

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References:

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[3]	Blum, J. R.; Kiefer, J.; Rosenblatt, M., Distribution free tests of independence based on the sample distribution function, Ann. Math. Statist., 32, 485-498 (1961) · Zbl 0139.36301
[4]	Deheuvels, P., Propriétés d’existence et propriétés topologiques des fonctions de dépendance avec applications à la convergence des types pour les lois multivariées, C.R. Acad. Sci. Paris Ser. A, 288, 145-148 (1979) · Zbl 0396.60019
[5]	Deheuvels, P., Non parametric tests of independence, (Raoult, J. P., Statistique non prmétrique symptotique. Statistique non prmétrique symptotique, Lecture Notes in Mathematics No. 821 (1980), Springer-Verlag: Springer-Verlag New York), 95-107 · Zbl 0455.62031
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[7]	Dugue, D., Sur des tests d’indépendance indépendants de la loi, C.R. Acad. Sci. Paris Ser. A, 281, 1103-1104 (1975) · Zbl 0401.62035
[8]	Hoeffding, W., A non parametric test for independence, Ann. Math. Statist., 19, 546-557 (1948) · Zbl 0032.42001
[9]	Kac, M.; Siegert, A. J.F, An explicit representation of a stationary Gaussian process, Ann. Math. Statist., 18, 438-442 (1947) · Zbl 0033.38501
[10]	Konijn, H. S., On the power of certain tests of independance in bivariate populations, Ann. Math. Statist., 27, 300-323 (1956) · Zbl 0075.29302
[11]	Koziol, J. A.; Nemec, A. F., On a Cramer-Von Mises type statistic for testing bivariate independence, Canad. J. Statist., 7, 43-52 (1979) · Zbl 0424.62027
[12]	Ruschendorf, L., Asymptotic distributions of multivariate rank order statistics, Ann. Statist., 4, 912-923 (1976) · Zbl 0359.62040
[13]	Ruymgaart, F. H.; Shorack, G. R.; van Zwet, W. R., Asymptotic normality of non parmatric tests of independence, Ann. Math. Statist., 43, 1122-1135 (1972) · Zbl 0254.62025

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