Multivariate transformed Gaussian processes

Yuan, Yan; Jeong, Jaehong; Genton, Marc G.

doi:10.1007/s42081-019-00068-6

Cited by 11 publications

(10 citation statements)

References 75 publications

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“…To assess the empirical power of the new test, we simulate data from the non-Gaussian sinh-arcsinh (SAS) transformed multivariate Matérn random field defined in Yan et al (2020). Specifically, we obtain the non-Gaussian data using the element-wise and inverse SAS transformation (Jones & Pewsey, 2009) on the data from Gaussian random fields, that is, the data used earlier for assessing the type I error.…”

Section: Type I Error and Empirical Power Of The New Testmentioning

confidence: 99%

“…Of course, all marginals being normal does not mean being jointly normal, so these marginal transformations may only partly help; in this case, we should be aware of the effect of conducting the current statistical procedures under the violated Gaussian assumption, and consider to switch to non-Gaussian methods (e.g. Xu &Genton, 2017 andYan et al, 2020).…”

Section: Wind Data Applicationmentioning

confidence: 99%

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Are You All Normal? It Depends!

Chen

Genton

2022

Int Statistical Rev

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Summary 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 utilises 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.

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Section: Type I Error and Empirical Power Of The New Testmentioning

confidence: 99%

Section: Wind Data Applicationmentioning

confidence: 99%

Are You All Normal? It Depends!

Chen

Genton

2022

Int Statistical Rev

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“…is defined by a N × 1 There are non-Gaussian spatial modeling approaches other than (a) and (b), including copula-based spatial modeling (e.g., Gräler, 2014), the Gaussian mixture approach (e.g., Fonseca and Steel, 2011), and approaches assuming non-Gaussian spatial processes (e.g., Zhang and El-Shaarawi, 2010). See Yan et al (2020) for a literature review.…”

Section: Additive Mixed Model (Amm)mentioning

confidence: 99%

“…According to Yan et al (2020), representative modeling approaches for non-Gaussian spatial data are classified with (a) variable transformation and (b) generalized linear modeling. The former converts explained variables, which have a non-Gaussian distribution, to Gaussian variables through a transformation function.…”

Section: Introductionmentioning

confidence: 99%

Compositionally-warped additive mixed modeling for a wide variety of non-Gaussian spatial data

Murakami

Kajita²,

Kajita³

et al. 2021

Spatial Statistics

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“…To assess the empirical power of the new test, we simulate data from the non-Gaussian sinh-arcsinh (SAS) transformed multivariate Matérn random field defined in Yan et al (2020).…”

Section: Type I Error and Empirical Power Of The New Testmentioning

confidence: 99%

Are You All Normal? It Depends!

Chen¹,

Genton²

2020

Preprint

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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 χ 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.

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Multivariate transformed Gaussian processes

Cited by 11 publications

References 75 publications

Are You All Normal? It Depends!

Are You All Normal? It Depends!

Compositionally-warped additive mixed modeling for a wide variety of non-Gaussian spatial data

Are You All Normal? It Depends!

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