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hypothesis of randomness; weak law of large numbers; randomized ranks; averaged scores

References:

[1] J. Hájek: **Asymptotic sufficiency of the vector of ranks in the Bahadur sense**. Ann. Statist. 2(1974), 1105-1125. MR 0356355

[2] M. Raghavachari: **On the theorem of Bahadur on the rate of convergence of test statistics**. Ann. Math. Statist. 41 (1970), 1695-1699. DOI 10.1214/aoms/1177696813 | MR 0266361

[3] G. G. Woodworth: **Large deviations and Bahadur efficiency of linear rank statistics**. Ann. Math. Statist. 41 (1970), 251-283. DOI 10.1214/aoms/1177697206 | MR 0264804 | Zbl 0211.50502

[4] D. Vorlíčková: **Asymptotic properties of rank tests under discrete distributions**. Z. Wahrscheinlichkeitstheorie. verw. Geb. 14 (1970), 275-289. DOI 10.1007/BF00533666 | MR 0269049