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Consistency and Unbiasedness of Certain Nonparametric Tests
Open accessAbstract
It is shown that there exist strictly unbiased and consistent tests for the univariate and multivariate two- and $k$-sample problem, for the hypothesis of independence, and for the hypothesis of symmetry with respect to a given point. Certain new tests for the univariate two-sample problem are discussed. The large sample power of these tests and of the Mann-Whitney test are obtained by means of a theorem of Hoeffding. There is a discussion of the problem of tied observations.
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Citations
Cited by
Use of Ranks in One-Criterion Variance Analysis
Kruskal, W. H., & Wallis, W. A. (1952) · Journal of the American Statistical Association · doi:10.1080/01621459.1952.10483441 · Cited by 13,912
A generalized Wilcoxon test for comparing arbitrarily singly-censored samples
Gehan, E. A. (1965) · Biometrika · doi:10.1093/biomet/52.1-2.203 · Cited by 3,406
On the Asymptotic Efficiency of Certain Nonparametric Two-Sample Tests
Mood, A. M. (1954) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177728719 · Cited by 406
Metadata
- Authors
- Lehmann, E. L.
- Venue
- The Annals of Mathematical Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 1951-06
- Volume
- 22
- Issue
- 2
- Pages
- 165-179
- ISSN
- 0003-4851 (ISSN-L)
- OpenAlex
- W2007438860
- Cited by
- 394
- References
- 0
- FWCI
- 13.92
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Lehmann, E. L. (1951). Consistency and Unbiasedness of Certain Nonparametric Tests. The Annals of Mathematical Statistics. https://doi.org/10.1214/aoms/1177729639
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
