论文标题
在结合零偏置变换和经验特征函数以测试正态性时
On combining the zero bias transform and the empirical characteristic function to test normality
论文作者
论文摘要
我们提出了一个新的强大的单变量正常测试家族。这些测试基于特征函数空间中的初始值问题，该功能源自零偏置转换中正态分布的固定点属性。测试统计量的限制分布在零假设以及连续和固定的替代方案下提供。使用从零分布中限制高斯过程的协方差结构，我们为限制随机元素的前四个累积物提供了显式公式，并通过拟合来自Pearson系统的分布来应用结果。一项比较的蒙特卡洛电力研究表明，新的测试是最强良好的测试的认真竞争者。
We propose a new powerful family of tests of univariate normality. These tests are based on an initial value problem in the space of characteristic functions originating from the fixed point property of the normal distribution in the zero bias transform. Limit distributions of the test statistics are provided under the null hypothesis, as well as under contiguous and fixed alternatives. Using the covariance structure of the limiting Gaussian process from the null distribution, we derive explicit formulas for the first four cumulants of the limiting random element and apply the results by fitting a distribution from the Pearson system. A comparative Monte Carlo power study shows that the new tests are serious competitors to the strongest well established tests.
