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Distribution-free confidence bounds for \(P(X < Y)\). (English) Zbl 0176.48606


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statistics
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[4] Chernoff, Hermann; Savage, I. Richard, Asymptotic normality and efficiency of certain nonparametric test statistics, Ann. Math. Statist., 29, 972-994 (1958) · Zbl 0092.36501 · doi:10.1214/aoms/1177706436
[5] Van Dantzig, D., On the consistency and the power of Wilcoxon’s two-sample test, Nederl. Akad. Wetensch. Verslag Afd. Natuurk., Series A, 54, No. 1, 1-9 (1951) · Zbl 0042.14401
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[7] Zakkula Govindarajulu, “Asymptotic normality of a class of test statistics,” unpublished manuscript, 1965. · Zbl 0225.62065
[8] Govindarajulu, Zakkula, On the distribution of sum of two independent Kolmogorov statistics, Sankhyã, Series A, 29, 61-82 (1967) · Zbl 0158.18501
[9] Govindarajulu, Zakkula, Two-sided confidence limits forP(X<Y) for normal samples ofX andY, Sankhyã, Series B, 29, 35-40 (1967)
[10] Z. Govindarajulu, L. Lecam and M. Raghavachari, “Generalizations of theorems of Chernoff-Savage on the asymptotic normality of test statistics,”Proc. Fifth Berkeley Symposium on Mathematical Statistics and Probability, 1, Univ. of Calif. Press at Berkeley and Los Angeles, (1966), 609-638.
[11] Lehmann, E. L., Consistency and unbiasedness of non-parametric tests, Ann. Math. Statist., 22, 165-179 (1951) · Zbl 0045.40903 · doi:10.1214/aoms/1177729639
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[14] Owen, D. B.; Craswell, K. J.; Hanson, D. L., Nonparametric upper confidence bounds forP(Y<X) and confidence limits forP(Y<X) whenX andY are normal, J. Amer. Statist. Ass., 59, 906-924 (1964) · Zbl 0127.10504 · doi:10.2307/2283110
[15] Sen, P. K., A note on asymptotically distribution-free confidence bounds forP(X<Y) based on two independent samples, Sankhyã, Series A, 29, Part I, 95-102 (1967) · Zbl 0173.20903
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