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September, 1978 A Robust Asymptotic Testing Model
Helmut Rieder
Ann. Statist. 6(5): 1080-1094 (September, 1978). DOI: 10.1214/aos/1176344312


In order to obtain quantitative results about the influence of outliers on tests, their maximum size and minimum power over certain neighborhoods are evaluated asymptotically. The neighborhoods are defined in terms of $\varepsilon$-contamination and total variation, the tests considered are based on statistics $n^{-\frac{1}{2}} \sum^n_{i=1} IC(x_i), IC$ a rather arbitrary function. Furthermore, the unique $IC^\ast$ is determined that leads to a maximin test with respect to this subclass of tests. A comparison with the likelihood ratio of least favorable pairs shows that the test based on $n^{-\frac{1}{2}}\sum^n_{i=1} IC^\ast(x_i)$ is in fact maximin among all tests at a given level. Tests based on $(M)$-statistics are also considered.


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Helmut Rieder. "A Robust Asymptotic Testing Model." Ann. Statist. 6 (5) 1080 - 1094, September, 1978.


Published: September, 1978
First available in Project Euclid: 12 April 2007

zbMATH: 0411.62020
MathSciNet: MR499574
Digital Object Identifier: 10.1214/aos/1176344312

Primary: 62G35
Secondary: 62E20

Keywords: $\varepsilon$-contamination , asymptotic maximin test , asymptotic normality , Asymptotic relative efficiency , contiguity , least favorable pair , Total variation

Rights: Copyright © 1978 Institute of Mathematical Statistics


Vol.6 • No. 5 • September, 1978
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