论文标题
你们都很正常吗？这取决于！
Are You All Normal? It Depends!
论文作者
论文摘要
正态性的假设基于统计数据的大部分发展，包括空间统计数据，并提出了许多测试。在这项工作中，我们专注于多元设置，并首先回顾了I.I.D.多变量正常测试的最新进展。数据，重点是偏度和峰度方法。我们通过模拟研究表明，其中一些测试不能直接用于测试空间数据的正态性。我们进一步简要审查了依赖性（时间或空间）下的少数现有单变量测试，然后通过考虑空间依赖性来提出新的多元正态性测试对空间数据。新的测试利用联合交流原理将原假设分解为投影数据的单变量正态性假设的交集，如果拒绝任何个人假设，它会拒绝多变量正态性。单变量正态性的单个假设是使用Jarque-Bera类型的测试统计量进行的，该统计统计统计数据是数据中空间依赖性的。我们还在模拟研究中表明，新测试对I型误差和高经验能力具有良好的控制，尤其是对于大型样本量。我们进一步说明了对阿拉伯半岛上双变量风数据的测试。
The assumption of normality has underlain much of the development of statistics, including spatial statistics, and many tests have been proposed. In this work, we focus on the multivariate setting and first review the recent advances in multivariate normality tests for i.i.d. data, with emphasis on the skewness and kurtosis approaches. We show through simulation studies that some of these tests cannot be used directly for testing normality of spatial data. We further review briefly the few existing univariate tests under dependence (time or space), and then propose a new multivariate normality test for spatial data by accounting for the spatial dependence. The new test utilizes the union-intersection principle to decompose the null hypothesis into intersections of univariate normality hypotheses for projection data, and it rejects the multivariate normality if any individual hypothesis is rejected. The individual hypotheses for univariate normality are conducted using a Jarque-Bera type test statistic that accounts for the spatial dependence in the data. We also show in simulation studies that the new test has a good control of the type I error and a high empirical power, especially for large sample sizes. We further illustrate our test on bivariate wind data over the Arabian Peninsula.
