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Article

Stoimenova, Eugenia
Two-sample rank tests based on exceeding observations. (English). Applications of Mathematics, vol. 52 (2007), issue 4, pp. 345-352
MSC: 62G10, 62G20 | MR 2324732 | Zbl 1164.62347 | DOI: 10.1007/s10492-007-0019-0
Keywords:
location problem; $E$-test statistic; $M$-test statistic
Summary:
Simple rank statistics are used to test that two samples come from the same distribution. Šidák’s $E$-test (Apl. Mat. 22 (1977), 166–175) is based on the number of observations from one sample that exceed all observations from the other sample. A similar test statistic is defined in Ann. Inst. Stat. Math. 52 (1970), 255–266. We study asymptotic behavior of the moments of both statistics.
References:
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[2] J.  Hájek, Z. Šidák: Theory of rank tests. Academic Press, Orlando, 1967. MR 0229351
[3] S.  Rosenbaum: Tables for a nonparametric test of location. Ann. Math. Stat. 25 (1954), 146–150. DOI 10.1214/aoms/1177728854 | MR 0061314 | Zbl 0056.37602
[4] Z.  Šidák: Tables for the two-sample location $E$-test based on exceeding observations. Apl. Mat. 22 (1977), 166–175. MR 0440791
[5] Z.  Šidák, J.  Vondráček: A simple non-parametric test of the difference in location of two populations. Apl. Mat. 2 (1957), 215–221. MR 0090203
[6] E.  Stoimenova: Rank tests based on exceeding observations. Ann. Inst. Stat. Math. 52 (2000), 255–266. DOI 10.1023/A:1004161721553 | MR 1763562 | Zbl 0959.62042
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