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Local efficiency of a Cramér-von Mises test of independence. (English) Zbl 1079.62048

Summary: P. Deheuvels [see Publ.Inst. Stat. Univ. Paris 26, 29–50 (1981; Zbl 0478.62029); Rev. Roum. Math. Pures Appl. 26, 213–226 (1981; Zbl 0477.62030); J. Multivariate Anal. 11, 102–113 (1981; Zbl 0486.62043)] proposed a rank test of independence based on a Cramér-von Mises functional of the empirical copula process. Using a general result on the asymptotic distribution of this process under sequences of contiguous alternatives, the local power curve of Deheuvels’ test is computed in the bivariate case and compared to that of competing procedures based on linear rank statistics. The J. Gil-Pelaez inversion formula [Biometrika 38, 481–482 (1951; Zbl 0045.07204)] is used to make additional comparisons in terms of a natural extension of Pitman’s measure of asymptotic relative efficiency.

MSC:

62G10 Nonparametric hypothesis testing
62G20 Asymptotic properties of nonparametric inference
62H15 Hypothesis testing in multivariate analysis
62H10 Multivariate distribution of statistics
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