Open Access
March, 1982 Qualitative Robustness of Rank Tests
Helmut Rieder
Ann. Statist. 10(1): 205-211 (March, 1982). DOI: 10.1214/aos/1176345703


An asymptotic notion of robust tests is studied which is based on the requirement of equicontinuous error probabilities. If the test statistics are consistent, their robustness in Hampel's sense and robustness of the associated tests turn out to be equivalent. Uniform extensions are considered. Moreover, test breakdown points are defined. The main applications are on rank statistics: they are generally robust, under a slight condition even uniformly so; their points of final breakdown coincide with the breakdown points of the corresponding $R$ - estimators.


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Helmut Rieder. "Qualitative Robustness of Rank Tests." Ann. Statist. 10 (1) 205 - 211, March, 1982.


Published: March, 1982
First available in Project Euclid: 12 April 2007

zbMATH: 0484.62054
MathSciNet: MR642732
Digital Object Identifier: 10.1214/aos/1176345703

Primary: 62G35
Secondary: 62E20 , 62G10

Keywords: breakdown points of tests and test statistics , consistency of tests and tests statistics , Equicontinuity of power functions and laws , gross errors , Kolmogorov , laws of large numbers for rank statistics , Levy , one-sample rank statistics , Prokhorov , total variation distances

Rights: Copyright © 1982 Institute of Mathematical Statistics

Vol.10 • No. 1 • March, 1982
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