Introduction and summary
In [5] and [6] the author proposed point estimates, tests and confidence procedures for the parameters in a linear model, which have the same asymptotic efficiency (relative to the corresponding classical methods) as the Wilcoxon test has relative to the t-test. Here, “asymptotic” refers to the case that the numbers of observations per cell tend to infinity; in practice, they should presumably be at least equal to four.
Received 23 August 1963.
This work was begun while the author was a Professor of the Adolph C. and Mary Sprague Miller Institute for Basic Research in Science, University of California, Berkeley, and was completed with the partial support of the Office of Naval Research, Contract N onr-222-(43). This paper in whole or in part may be reproduced for any purpose of the United States Government.
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References
FRIEDMAN, M. (1937). The use of ranks to avoid the assumption of normality implicit in the analysis of variance. J. Amer. Statist. Assoc. 32 675–701.
HODGES, J. L., Jr. and LEHMANN, E. L. (1961). Comparison of the normal scores and Wilcoxon tests. Proc. Fourth Berkeley Symp. Math. Statist. Prob. 1 307–317.
HODGES, J. L., Jr. and LEHMANN, E. L. (1962). Rank methods for combination of independent experiments in analysis of variance. Ann. Math. Statist. 33 482–497.
HODGES, J. L., Jr. and LEHMANN, E. L. (1963). Estimates of location based on rank tests. Ann. Math. Statist. 34 598–611.
LEHMANN, E. L. (1963). Robust estimation in analysis of variance. Ann. Math. Statist. 34 957–966.
LEHMANN, E. L. (1963). Asymptotically nonparametric inference: an alternative approach to linear models. Ann. Math. Statist. 34 1494–1506.
LEHMANN, E. L. (1963). Nonparametric confidence intervals for a shift parameter. Ann. Math. Statist. 34 1507–1512.
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Lehmann, E.L. (2012). Asymptotically Nonparametric Inference in Some Linear Models with one Observation per Cell. 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_49
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