This paper introduces and investigates powerful omnibus test for uniformity and compares it with some classical and recent solutions. All statistics under consideration are weighted functionals of the classical empirical process. The goal is to provide a quantitative comparison of tests under consideration and to study real possibilities of using them to detect departures from the hypothesised distribution that occur in the tails. The newly introduced concept of pathwise variant of intermediate efficiency serves to achieve the goal. This contribution covers the case when under the alternative a moderately large portion of probability mass is allocated towards the tails. It is demonstrated that the approach allows for tractable, analytic comparison between the given test and the benchmark, and for reliable quantitative evaluation of weighted statistics. Finite sample results illustrate the proposed approach and confirm the theoretical findings.

中文翻译：

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一些加权拟合优度统计的中间效率

本文介绍并研究了强大的统一性综合测试，并将其与一些经典和最新的解决方案进行了比较。所考虑的所有统计数据都是经典经验过程的加权泛函。目标是提供正在考虑的测试的定量比较，并研究使用它们来检测尾部发生的假设分布的偏离的实际可能性。新引入的中间效率的路径变体概念有助于实现目标。这种贡献涵盖了在替代方案下将概率质量的中等大部分分配给尾部的情况。证明该方法允许在给定测试和基准之间进行易处理的分析比较，以及对加权统计的可靠定量评估。有限样本结果说明了所提出的方法并证实了理论发现。