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Rank Score Comparison of Several Regression Parameters
J. N. Adichie
The Annals of Statistics
Vol. 2, No. 2 (Mar., 1974), pp. 396-402
Published by: Institute of Mathematical Statistics
Stable URL: http://www.jstor.org/stable/2958050
Page Count: 7
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For testing βi = β, i = 1,⋯, k, in the model Yij = α + βiX ij + Zij j = 1,⋯, ni a class of rank score tests is presented. The test statistic is based on the simultaneous ranking of all the observations in the different k samples. Its asymptotic distribution is proved to be chi square under the hypothesis and noncentral chi square under an appropriate sequence of alternatives. The asymptotic efficiency of the given procedure relative to the least squares procedure is shown to be the same as the efficiency of rank score tests relative to the t-test in the two sample problem. The proposed criterion would be an asymptotically most powerful rank score test for the hypothesis if the distribution function of the observations is known.
The Annals of Statistics © 1974 Institute of Mathematical Statistics