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Pointwise versus uniform robustness of some large-sample tests and confidence intervals. (English) Zbl 0724.62037
The purpose of this paper is to illustrate the fact that it is typical for many large-sample tests to be pointwise robust but not uniformly robust, even for seemingly narrow classes of the underlying distributions. Two cases, the one sample t-test and confidence intervals for the binomial proportion p, are treated in detail.
It is shown that the t-test is not uniformly robust if the underlying family of distributions consists of distributions within a Kolmogorov neighborhood of an arbitrary distribution or those with densities supported in a finite interval. In the binomial case it is shown that the standard confidence intervals constructed using the delta method are not uniformly robust if the underlying family of distributions consists of all binomial distributions with $$0<p<1$$.
Reviewer: J.Antoch (Praha)

##### MSC:
 62F35 Robustness and adaptive procedures (parametric inference) 62F25 Parametric tolerance and confidence regions 62G35 Nonparametric robustness