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June, 1983 Galton's Test as a Linear Rank Test with Estimated Scores and Its Local Asymptotic Efficiency
Konrad Behnen, Georg Neuhaus
Ann. Statist. 11(2): 588-599 (June, 1983). DOI: 10.1214/aos/1176346164


In the general two-sample testing problem $F = G$ versus $F \leq G, F \neq G$ the shift-model score function $f' \circ F^{-1}/f \circ F^{-1}$ has to be replaced by the nonparametric score function $b = \bar{f} - \bar{g}$, where $\bar{f} = d(F \circ H^{-1})/dx, \bar{g} = d(G \circ H^{-1})/dx, H = (mF + nG)/(m + n)$, and adaption of linear rank tests should be based on rank estimators of $b$. We consider an easy but rough and inconsistent rank estimator of $b$. The resulting rank test turns out to be a generalization of Galton's test. A formula for local asymptotic power under arbitrary local alternatives is derived which allows for comparison of Galton's test with every linear rank test. For various types of alternatives the Galton test is compared with the optimal linear rank test and with the Wilcoxon test. In order to get an impression of the validity of extrapolation to finite sample sizes, we included a Monte Carlo study under the same types of fixed alternatives.


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Konrad Behnen. Georg Neuhaus. "Galton's Test as a Linear Rank Test with Estimated Scores and Its Local Asymptotic Efficiency." Ann. Statist. 11 (2) 588 - 599, June, 1983.


Published: June, 1983
First available in Project Euclid: 12 April 2007

zbMATH: 0531.62042
MathSciNet: MR696070
Digital Object Identifier: 10.1214/aos/1176346164

Primary: 62G10
Secondary: 62E25 , 62G20

Keywords: adaptive rank tests , estimated scores , Galton test , power simulation and extrapolation , stochastically-larger-alternatives , two-sample problem

Rights: Copyright © 1983 Institute of Mathematical Statistics


Vol.11 • No. 2 • June, 1983
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