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Qualitative Robustness of Tests

Diane Lambert
Journal of the American Statistical Association
Vol. 77, No. 378 (Jun., 1982), pp. 352-357
DOI: 10.2307/2287252
Stable URL: http://www.jstor.org/stable/2287252
Page Count: 6
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Qualitative Robustness of Tests
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Abstract

A test is qualitatively robust by definition if its sequence of -n-1log transformed P values, n being a measure of the sample size, is continuous as a point function of the observations and weakly equicontinuous as a function of discrete probability measures. This definition is applicable both to unconditional and to conditional tests. Under weak regularity conditions, an unconditional test is qualitatively robust if and only if its test statistic is continuous; a counterexample shows that conditional tests do not share this property. The sample mean, Student's t and Ȳ - X̄ permutation tests are not qualitatively robust; the sign, Wilcoxon, Huber censored likelihood, and normal scores tests are qualitatively robust.

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