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Rank estimators of scores for testing independence. (English) Zbl 0606.62045
For testing independence in the case of i.i.d. bivariate random variables with continuous distribution function, linear rank statistics are known to be asymptotically optimal for non-parametric alternatives, if the score function corresponds to the type of alternative.
Therefore we estimate such non-parametric score functions on the basis of ranks, give some convergence results on the estimators, and prove asymptotic normality of the resulting adaptive rank statistics under the null hypothesis and under fixed alternatives. Similar results for the two sample case are given by K. Behnen, G. Neuhaus and F. Ruymgaart [Ann. Stat. 11, 1175-1189 (1983; Zbl 0548.62029)] and by the first two authors [Commun. Stat., Theory Methods 13, 305-325 (1984; Zbl 0592.62036)].

62G05 Nonparametric estimation
62E20 Asymptotic distribution theory in statistics
62G10 Nonparametric hypothesis testing