Summary
It is shown that there exist strictly unbiased and consistent tests for the univariate and multivariate two- and fc-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. Thereāis a discussion of the problem of tied observations.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
H. C. Mathisen, āA method of testing the hypothesis that two samples are from the same population,ā Annals of Math. Stat., Vol. 14 (1943), pp. 188ā194.
W. Hoeffding, āA class of statistics with asymptotically normal distributions,ā Annals of Math. Stat., Vol. 19 (1948), pp. 293ā325.
H. B. Mann and D. R. Whitney, āOn a test of whether one of two random variables is stochastically larger than the other,ā Annals of Math. Stat,, Vol. 18 (1947), pp. 50ā60.
W. R. Thompson, āBiological applications of normal range and associated significance tests in ignorance of original distribution forms,ā Annals of Math. Stat., Vol. 9 (1938), pp. 281ā287.
W. Hoeffding, āA non-parametric test of independence,ā Annals of Math. Stat., Vol. 19 (1948), pp. 546ā557.
P. R. Halmos, āThe theory of unbiased estimation,ā Annals of Math. Stat., Vol. 17 (1946), pp. 34ā43.
E. L. Lehmann and H. ScheffĆ©, āCompleteness, similar regions, and unbiased estimationāPart I,ā Sankhyd, Vol. 10 (1950), pp. 305ā340.
E. L. Lehmann and H. ScheffĆ©, āCompleteness, similar regions, and unbiased estimation, Part II,ā unpublished.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
This chapter is published under an open access license. Please check the 'Copyright Information' section either on this page or in the PDF for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.
Copyright information
Ā© 2012 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Lehmann, E.L. (2012). Consistency and Unbiasedness of Certain Nonparametric Tests. In: Rojo, J. (eds) Selected Works of E. L. Lehmann. Selected Works in Probability and Statistics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-1412-4_32
Download citation
DOI: https://doi.org/10.1007/978-1-4614-1412-4_32
Published:
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4614-1411-7
Online ISBN: 978-1-4614-1412-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)