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On the limiting distribution of and critical values for the Hoeffding, Blum, Kiefer, Rosenblatt independence criterion. (English) Zbl 0569.62014
Tests of independence of random variables have been constructed by W. Hoeffding [Ann. Math. Stat. 19, 546-557 (1948; Zbl 0032.420)] and by J. R. Blum, J. Kiefer and M. Rosenblatt [ibid. 32, 485- 498 (1961; Zbl 0139.363)]. The present paper studies the asymptotic distributions of the statistics used in these tests of independence, and gives limiting critical values for the statistics.
Reviewer: L.Weiss

62E20 Asymptotic distribution theory in statistics
62G10 Nonparametric hypothesis testing
62H10 Multivariate distribution of statistics
62H15 Hypothesis testing in multivariate analysis