It is realized that existing powerful tests of goodness-of-fit are all based on sorted uniforms and, consequently, can suffer from the confounded effect of different locations and various signal frequencies in the deviations of the distributions under the alternative hypothesis from those under the null. This paper proposes circularly symmetric tests that are obtained by circularizing reweighted Anderson-Darling tests, with the focus on the circularized versions of Anderson-Darling and Zhang test statistics. Two specific types of circularization are considered, one is obtained by taking the average of the corresponding so-called scan test statistics and the other by using the maximum. To a certain extent, this circularization technique effectively eliminates the location effect and allows the weights to focus on the various signal frequencies. A limited but arguably convincing simulation study on finite-sample performance demonstrates that the circularized Zhang method outperforms the circularized Anderson-Darling and that the circularized tests outperform their parent methods. Large-sample theoretical results are also obtained for the average type of circularization. The results show that both the circularized Anderson-Darling and circularized Zhang have asymptotic distributions that are a weighted sum of an infinite number of independent squared standard normal random variables. In addition, the kernel matrices and functions are circulant. As a result, asymptotic approximations are computationally efficient via the fast Fourier transform.
翻译:人们认识到,现有强大的健康测试都以分类制服为基础,因此,在不同地点和不同信号频率的偏差中,可能会受到不同地点和不同信号频率的混混效应的影响,在替代假设下分布的偏差中,本论文建议通过循环加权的Anderson-Darling测试,以循环的Anderson-Darling和Zhang测试数据版本为重点,进行循环的对称测试,考虑两种特定的循环类型,一种是采用相应的所谓扫描测试统计数据的平均值,另一种是使用最大程度的。在某种程度上,这种循环化技术有效地消除了位置效应,并允许对各种信号频率的分量进行重力。关于有限但有说服力的模拟研究表明,循环的Zhang方法比循环的Anderson-Darling和Zhang测试版本版本的分解版本更完美,循环测试也超越了其母体方法。在平均循环类型中还获得了大量模拟的理论结果。结果显示,循环的Anderson-Dalbuildal-Dal-albal-alendalalalal-alalal-travelildal-traxal-rmalal-traxal-saltraxal-slal-slal-slal-smal-smlupaldaldaldaldal-smal-smal-smalxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx