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March, 1974 Rank Score Comparison of Several Regression Parameters
J. N. Adichie
Ann. Statist. 2(2): 396-402 (March, 1974). DOI: 10.1214/aos/1176342676


For testing $\beta_i = \beta, i = 1,\cdots, k$, in the model $Y_{ij} = \alpha + \beta_iX_{ij} + Z_{ij} j = 1,\cdots, n_i$ 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.


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J. N. Adichie. "Rank Score Comparison of Several Regression Parameters." Ann. Statist. 2 (2) 396 - 402, March, 1974.


Published: March, 1974
First available in Project Euclid: 12 April 2007

zbMATH: 0277.62051
MathSciNet: MR423669
Digital Object Identifier: 10.1214/aos/1176342676

Primary: 62G10
Secondary: 62E20 , 62G20 , 62J05

Keywords: Asymptotic efficiency , asymptotic normality , bounded in probability , orthogonal transformation , score generating function , Simultaneous ranking

Rights: Copyright © 1974 Institute of Mathematical Statistics


Vol.2 • No. 2 • March, 1974
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