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Robustness and power of parametric, nonparametric, robustified and adaptive tests—The multi-sample location problem

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This paper deals with a survey of different types of tests, parametric, nonparametric, robustified and adaptive ones, and with an application to the two-sided c-sample location problem. Some concepts of robustness are discussed, such as breakdown point, influence function, gross-error sensitivity and especially α- and β-robustness. A robustness study on level α in the case of heteroscedasticity and nonnormal distributions is carried out via Monte Carlo methods and also a power comparison of all the tests considered. It turns out that robustified versions of the F-test and Welch-test where the original observations are replaced by its ranks behave well over a broad class of distributions, symmetric ones with different tail weight and asymmetric ones, but, on the whole, an adaptive test is to prefer.

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  1. Institut für Statistik und Ökonometrie, Etuie Universität Berlin, Boltzmannstraße 20, 14195, Berlin, Germany

    Herbert Büning

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Büning, H. Robustness and power of parametric, nonparametric, robustified and adaptive tests—The multi-sample location problem. Statistical Papers 41, 381–407 (2000). https://doi.org/10.1007/BF02925759

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