Abstract
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.
Keywords
UnivariateMathematicsNonparametric statisticsConsistency (knowledge bases)StatisticsStatistical hypothesis testingEconometricsSample (material)Independence (probability theory)Multivariate statisticsDiscrete mathematics
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Publication Info
- Year
- 1951
- Type
- article
- Volume
- 22
- Issue
- 2
- Pages
- 165-179
- Citations
- 391
- Access
- Closed
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Cite This
E. L. Lehmann
(1951).
Consistency and Unbiasedness of Certain Nonparametric Tests.
The Annals of Mathematical Statistics
, 22
(2)
, 165-179.
https://doi.org/10.1214/aoms/1177729639
Identifiers
- DOI
- 10.1214/aoms/1177729639