The Annals of Statistics

Qualitative Robustness of Rank Tests

Helmut Rieder

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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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Ann. Statist., Volume 10, Number 1 (1982), 205-211.

First available in Project Euclid: 12 April 2007

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Primary: 62G35: Robustness
Secondary: 62E20: Asymptotic distribution theory 62G10: Hypothesis testing

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


Rieder, Helmut. Qualitative Robustness of Rank Tests. Ann. Statist. 10 (1982), no. 1, 205--211. doi:10.1214/aos/1176345703.

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