dc.contributor.author Chen, Wanfang dc.contributor.author Genton, Marc G. dc.date.accessioned 2020-09-14T06:06:04Z dc.date.available 2020-09-14T06:06:04Z dc.date.issued 2020-08-25 dc.identifier.uri http://hdl.handle.net/10754/665110 dc.description.abstract 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 we first provide a synopsis of 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, since the multivariate sample skewness and kurtosis measures, such as the Mardia's measures, deviate from their theoretical values under Gaussianity due to dependence, and some related tests exhibit inflated type I error, especially when the spatial dependence gets stronger. We review briefly the few existing tests under dependence (time or space), and then propose a new multivariate normality test for spatial data by accounting for the spatial dependence of the observations in the test statistic. The new test aggregates univariate Jarque-Bera (JB) statistics, which combine skewness and kurtosis measures, for individual variables. The asymptotic variances of sample skewness and kurtosis for standardized observations are derived given the dependence structure of the spatial data. Consistent estimators of the asymptotic variances are then constructed for finite samples. The test statistic is easy to compute, without any smoothing involved, and it is asymptotically $\chi^2_{2p}$ under normality, where $p$ is the number of variables. The new test has a good control of the type I error and a high empirical power, especially for large sample sizes. dc.publisher arXiv dc.relation.url https://arxiv.org/pdf/2008.10957 dc.rights Archived with thanks to arXiv dc.title Are You All Normal? It Depends! dc.type Preprint dc.contributor.department Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division dc.contributor.department Spatio-Temporal Statistics and Data Analysis Group dc.contributor.department Statistics Program dc.eprint.version Pre-print dc.identifier.arxivid 2008.10957 kaust.person Chen, Wanfang kaust.person Genton, Marc G. refterms.dateFOA 2020-09-14T06:06:53Z
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