This paper takes a look at omnibus tests of goodness of fit in the context of reweighted Anderson-Darling tests and makes threefold contributions. The first contribution is to provide a geometric understanding. It is argued that the test statistic with minimum variance for exchangeable distributional deviations can serve as a good general-purpose test. The second contribution is to propose better omnibus tests, called circularly symmetric tests and obtained by circularizing reweighted Anderson-Darling test statistics or, more generally, test statistics based on the observed order statistics. The resulting tests are called circularized tests. A limited but arguably convincing simulation study on finite-sample performance demonstrates that circularized tests have good performance, as they typically outperform their parent methods in the simulation study. The third contribution is to establish new large-sample results.

翻译：本文在加权重整安德森-达林检验的框架下探讨了拟合优度的综合检验，并做出三重贡献。第一项贡献是提供几何意义上的理解。研究表明，针对可交换分布偏离具有最小方差的检验统计量可作为有效的通用检验。第二项贡献是提出更优的综合检验方法，即通过环形化加权重整的安德森-达林检验统计量（或更一般地，基于观测顺序统计量的检验统计量）所获得的循环对称检验。由此得到的检验被称为环形化检验。一项范围有限但具有说服力的有限样本性能模拟研究显示，环形化检验表现优异，在模拟中通常优于其原始方法。第三项贡献是建立了新的大样本理论结果。