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

将经典的非参数k样本相等假设推广到k样本近似相等假设，并在k样本局部渐近粗差模型下研究了秩检验序列的渐近性质.我们的研究结果表明，经典的最优秩检验是敏感的偏离相当严格的平等的假设，因此，他们的使用是危险的，在实际情况下，可能会发生偏差。从实际应用的角度来看，研究k样本近似相等秩检验的稳健性也是很重要的，然后利用优控制方法可以很有效地构造渐近水平的α秩检验并给出其渐近最小功效的下界.本文提出的新思想和优化方法对于克服k样本情形下的特殊困难是必要的。本文从Huber稳健检验理论的角度出发，建立了k个位置参数在粗差存在下的稳健滑移检验问题。在稳健滑动检验问题的渐近模型下，利用优控制方法构造了基于k线性秩统计量的渐近水平α滑动秩检验，并利用弱优控制方法求出了其渐近最小功效.它还表明，滑动秩检验是渐近无偏的。

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.