Abstract
Rank tests based on the maximum number of exceeding observations for several standard nonparametric hypotheses are proposed. An approach to constructing nonparametric rank tests via metrics on the permutation group is used. The test statistics are based on a metric induced by Chebyshev's norm.
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References
Critchlow, D. (1985). Metric Methods for Analyzing Partially Ranked Data, Lecture Notes in Statist., No. 34, Springer, New York.
Critchlow, D. E. (1986). A unified approach to constructing nonparametric rank tests, Tech. Report. No. 86-15, Dept. of Statistics, Purdue University, Indiana.
Critchlow, D. E. (1992). On rank statistics: An approach via metrics on the permutation group, J. Statist. Plann. Inference, 32, 325–346.
Diaconis, P. (1988). Group Representations in Probability and Statistics, IMS Lecture Notes-Monograph Series, Vol. 11, Hayward, California.
Fueda, K. (1993). Spearman's rank correlation type two-sample test, Memories of the Faculty of Science, Kyushu University, Ser. A, 47,(1), 27–39.
Fueda, K. (1996). The limiting normality of the test statistic for the two-sample problem induced by a convex sum distance, Ann. Inst. Statist. Math., 48,(2), 337–347.
Haga, T. (1960). A two-sample rank test on location, Ann. Inst. Statist. Math., 11, 211–219.
Hajek, J. and Sidak, Z. (1967). Theory of Rank tests, Academic Press, New York.
Rosenbaum, S. (1957) Tables for a nonparametric test of location, Ann. Math. Statist., 25, 146–150.
Sidak, Z. (1977). Tables for the two-sample location E-test based on exceeding observations, Aplikace Matematiky, 22, 166–175.
Sidak, Z. and Vondracek, J. (1957). A simple non-parametric test of the difference in location of two populations, Aplikace Maternatiky, 2, 215–221.
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Stoimenova, E. Rank Tests Based on Exceeding Observations. Annals of the Institute of Statistical Mathematics 52, 255–266 (2000). https://doi.org/10.1023/A:1004161721553
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DOI: https://doi.org/10.1023/A:1004161721553