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.
Publié le : 1982-03-14
Classification:
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,
62G35,
62E20,
62G10
@article{1176345703,
author = {Rieder, Helmut},
title = {Qualitative Robustness of Rank Tests},
journal = {Ann. Statist.},
volume = {10},
number = {1},
year = {1982},
pages = { 205-211},
language = {en},
url = {http://dml.mathdoc.fr/item/1176345703}
}
Rieder, Helmut. Qualitative Robustness of Rank Tests. Ann. Statist., Tome 10 (1982) no. 1, pp. 205-211. http://gdmltest.u-ga.fr/item/1176345703/