Testing normality of data on a multivariate grid

Horváth, Lajos; Kokoszka, Piotr; Wang, Shixuan

doi:10.1016/j.jmva.2020.104640

Cited by 7 publications

(32 citation statements)

References 38 publications

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“…We note that for the samples of the 3‐month's mean SIS radiation and a significance level of

α = 0.05

, the test by Horváth et al . (2020) rejects the null hypothesis of a Gaussian distribution in merely 6 of the 33 years, marked by the P ‐values in italics. This means that for most years, the 3‐month's mean of the summer months can actually be assumed to be Gaussian, which is a consequence of a general central limit theorem principle.…”

Section: Application To Surface Incoming Shortwave Radiationmentioning

confidence: 94%

“…Our results suggest that the power of the test is similar to that of the functional time‐series case considered in Górecki et al (2018) and the scalar spatial case studied in Horváth et al . (2020).…”

Section: Finite‐sample Performancementioning

confidence: 99%

“…Horváth et al . (2020) analyzed mean monthly sea surface temperature data from various regions of the world and came to the conclusion that one needs to be cautious when assuming Gaussianity of spatial data. We want to explore what is revealed by the application of our test to an important dataset.…”

Section: Application To Surface Incoming Shortwave Radiationmentioning

confidence: 99%

“…For comparison, we use the test of Horváth et al . (2020) with the power estimator of the covariances. In order to guarantee comparability, we use the same truncation parameter as for our functional test.…”

Section: Application To Surface Incoming Shortwave Radiationmentioning

confidence: 99%

“…Horváth et al . (2020) derived a normality test for a scalar spatial field, which falls into a broad Jarque–Bera family of tests. This test is based on the asymptotic distribution of suitably defined skewness and kurtosis.…”

Section: Introductionmentioning

confidence: 99%

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Testing normality of spatially indexed functional data

2021

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We develop a test of normality for spatially indexed functions. The assumption of normality is common in spatial statistics, yet no significance tests, or other means of assessment, have been available for functional data. This article aims at filling this gap in the case of functional observations on a spatial grid. Our test compares the moments of the spatial (frequency domain) principal component scores to those of a suitable Gaussian distribution. Critical values can be readily obtained from a chi‐squared distribution. We provide rigorous theoretical justification for a broad class of weakly stationary functional random fields. We perform simulation studies to assess the power of the test against various alternatives. An application to surface incoming shortwave radiation illustrates the practical value of this procedure.

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“…We note that for the samples of the 3‐month's mean SIS radiation and a significance level of

α = 0.05

Section: Application To Surface Incoming Shortwave Radiationmentioning

confidence: 94%

Section: Finite‐sample Performancementioning

confidence: 99%

Section: Application To Surface Incoming Shortwave Radiationmentioning

confidence: 99%

Section: Application To Surface Incoming Shortwave Radiationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Testing normality of spatially indexed functional data

2021

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A neural network-based adaptive cut-off approach to normality testing for dependent data

Kim,

Genton,

Huser

et al. 2024

Stat Comput

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There is a wide availability of methods for testing normality under the assumption of independent and identically distributed data. When data are dependent in space and/or time, however, assessing and testing the marginal behavior is considerably more challenging, as the marginal behavior is impacted by the degree of dependence, which typically leads to an inflation in Type I error rates. We propose a new approach to assess normality for dependent data by non-linearly incorporating existing statistics from normality tests as well as sample moments such as skewness and kurtosis through a neural network with adaptive cut-offs by which the Type I error inflation issue is fixed. We calibrate (deep) neural networks by simulated normal and non-normal data with a wide range of dependence structures and we determine the probability of rejecting the null hypothesis. We compare several approaches for normality tests and demonstrate the superiority of our method in terms of statistical power through an extensive simulation study. A real world application to global temperature data further demonstrates how the degree of spatio-temporal aggregation affects the marginal normality in the data.

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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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Testing normality of data on a multivariate grid

Cited by 7 publications

References 38 publications

Testing normality of spatially indexed functional data

Testing normality of spatially indexed functional data

A neural network-based adaptive cut-off approach to normality testing for dependent data

Are You All Normal? It Depends!

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