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- W2189199 abstract "The true level an(F) of a test at nominal level a and sample size n is said to be pointwise robust if an(F)→a as n→ ∞ for each distribution F. If F is unknown and only assumed to belong to the class ℱ of distributions, one may wish to consider the level to be defined by an=supℱ an (F). The test is said to be uniformly robust over ℱ if an→a as n→∞. Corresponding definitions apply to the coverage probabilities of confidence intervals. The purpose of this paper is to illustrate the fact that it is typil for many large-sample tests to be pointwise robust but not uniformly robust, even for seemingly narrow classes ℱ 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 ℱ consists of distributions within a Kolmogorov neighbourhood of an arbitrary distribution or those with densities supported in a finite interval. The test is uniformly robust if ℱ is a set of distributions with uniformly bounded standardized moments. In the binomial case it is shown that the standard confidence intervals constructed using the delta method are not uniformly robust if ℱ consists of all binomial distributions with 0<p<l." @default.
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- W2189199 date "2011-11-19" @default.
- W2189199 modified "2023-09-23" @default.
- W2189199 title "Pointwise Versus Uniform Robustness of Some Largesample Tests and Confidence Intervals" @default.
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- W2189199 doi "https://doi.org/10.1007/978-1-4614-1412-4_51" @default.
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