The testing problems of hypothesis of k sample approximate equality in the presence of gross errors

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We extend the classical nonparametric hypothesis of k sample equality to a hypothesis of k sample approximate equality and explore the asymptotic properties of sequences of rank tests under a k-sample local asymptotic gross error model. Our results reveal that the classical optimum rank tests are sensitive to deviation from the assumptions of rather stringent equality, and hence their use is dangerous in practical situations where deviation may occur. The study of the robustness of rank tests for k-sample approximate equality is also important from the point of view of practical applications, and then the majorization methods can be quite effectively utilized for constructing asymptotic level α rank tests and giving the lower bounds for their asymptotic minimum powers. We should emphasize that the new ideas and majorization devices developed in this paper are essential for overcoming the peculiar difficulties arising in the k-sample case.A robust slippage test problem of k location parameters in the presence of gross errors is formulated from the point of view of Huber's robust test theory. Under an asymptotic model of the robust slippage test problem an asymptotic level α slippage rank test based on k linear rank statistics is constructed by applying majorization methods and its asymptotic minimum power evaluated by applying weak majorization methods. It is also shown that the slippage rank test is asymptotically unbiased.