×

Linear rank score statistics when ties are present. (English) Zbl 0931.62041

Summary: The normalized versions of distribution functions are used to derive an asymptotic theory of rank statistics including ties. A mixed model which permits almost arbitrary dependencies is considered. Moreover, a Chernoff-Savage theorem in the presence of ties is proven.

MSC:

62G20 Asymptotic properties of nonparametric inference
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Akritas, M. G.; Arnold, S. F.; Brunner, E., Nonparametric hypotheses and rank statistics for unbalanced factorial designs, J. Amer. Statist. Assoc., 92, 258-265 (1997) · Zbl 0890.62038
[2] Akritas, M. G.; Brunner, E., A unified approach to rank tests for mixed models, J. Statist. Plann. Inference, 61, 249-279 (1997) · Zbl 0872.62051
[3] Behnen, K., Asymptotic comparision of rank tests for the regression problem when ties are present, Ann. Statist., 4, 157-174 (1976) · Zbl 0321.62048
[4] Boos, D. D.; Brownie, C., A rank-based mixed model approach to multisite clinical trials, Biometrics, 48, 61-72 (1992)
[5] Brunner, E.; Denker, M., Rank statistics under dependent observations and applications to factorial designs, J. Statist. Plann. Inference, 42, 353-378 (1994) · Zbl 0816.62035
[6] Brunner, E.; Puri, M. L., Nonparametric methods in design and analysis of experiments, (Handbook of Statistics, vol. 13 (1996), North-Holland: North-Holland Amsterdam), 631-703 · Zbl 0920.62058
[7] Brunner, E.; Puri, M. L.; Sun, S., Nonparametric methods for stratified two-sample designs with application to multi clinic trials, J. Amer. Statist. Assoc., 90, 1004-1014 (1995) · Zbl 0843.62102
[8] Bühler, W. J., The treatment of ties in the Wilcoxon test, Ann. Math. Statist., 38, 519-522 (1967) · Zbl 0161.38004
[9] Chanda, K. C., On the efficiency of the two-sample Mann-Whitney test for discrete populations, Ann. Math. Statist., 34, 612-617 (1963) · Zbl 0192.26202
[10] Chemoff, H.; Savage, I., Asymptotic normality and efficiency of certain nonparametric test statistics, Ann. Math. Statist., 29, 972-994 (1958) · Zbl 0092.36501
[11] Conover, W. J., Rank tests for one sample, two samples, and \(k\) samples without the assumption of a continuous distribution function, Ann. Statist., 1, 1105-1125 (1973) · Zbl 0275.62042
[12] Hoeffding, W., On the centering of a simple linear rank statistic, Ann. Statist., 1, 54-66 (1973) · Zbl 0255.62015
[13] Munzel, U., Asymptotische Normalität Linearer Rangstatistiken bei Bindungen unter Abhängigkeit, (Diploma Thesis. Inst. f. Mathematische Stochastik (1994), Universität Göttingen)
[14] Putter, J., The treatment of ties in some nonparametric tests, Ann. Math. Statist., 26, 368-386 (1955) · Zbl 0065.12302
[15] Vorličková, D., Asymptotic properties of rank tests under discrete distributions, Z. Wahrscheinlichkeitstheorie Verwandte Gebiete, 14, 275-289 (1970) · Zbl 0193.17303
[16] Vorličková, D., Asymptotic properties of rank tests of symmetry under discrete distributions, Ann. Math. Statist., 43, 2013-2018 (1972) · Zbl 0263.62030
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.