Tests of fit to exact models in statistical analysis often lead to rejections even when the model is a useful approximate description of the random generator of the data. Among possible relaxations of a fixed model, the one defined by contamination neighbourhoods has received much attention, from its central role in Robust Statistics. For probabilities on the real line, consistent tests of fit to a contamination neighbourhood of a fixed model can be based on the minimal Kolmogorov distance between the model and the set of trimmings of the underlying random generator. We provide some alternative formulations for this functional in terms of a variational problem. As a consequence, a test of fit to contamination neighbourhoods can be effectively implemented. Also, we prove a result of directional differentiability giving the theoretical basis for the study of the asymptotic properties of such test.

中文翻译：

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Lipschitz 正则化的 Box-Constrained Monotone Approximations，在稳健测试中的应用

统计分析中对精确模型的拟合测试通常会导致拒绝，即使模型是对数据随机生成器的有用近似描述。在固定模型的可能松弛中，由污染邻域定义的模型因其在稳健统计中的核心作用而备受关注。对于实线上的概率，固定模型污染邻域的一致拟合测试可以基于模型与底层随机生成器的修整集之间的最小 Kolmogorov 距离。我们根据变分问题为这个泛函提供了一些替代公式。因此，可以有效地实施对污染社区的拟合测试。还，