JOURNAL OF MULTIVARIATE ANALYSIS | 卷:179 |
Testing normality of data on a multivariate grid | |
Article | |
Horvath, Lajos1  Kokoszka, Piotr2  Wang, Shixuan3  | |
[1] Univ Utah, Dept Math, Salt Lake City, UT 84112 USA | |
[2] Colorado State Univ, Dept Stat, Ft Collins, CO 80523 USA | |
[3] Univ Reading, Dept Econ, Reading RG6 6AA, Berks, England | |
关键词: Gaussian process; Lattice data; Significance test; Spatial statistics; | |
DOI : 10.1016/j.jmva.2020.104640 | |
来源: Elsevier | |
【 摘 要 】
We propose a significance test to determine if data on a regular d-dimensional grid can be assumed to be a realization of Gaussian process. By accounting for the spatial dependence of the observations, we derive statistics analogous to sample skewness and kurtosis. We show that the sum of squares of these two statistics converges to a chi-square distribution with two degrees of freedom. This leads to a readily applicable test. We examine two variants of the test, which are specified by two ways the spatial dependence is estimated. We provide a careful theoretical analysis, which justifies the validity of the test for a broad class of stationary random fields. A simulation study compares several implementations. While some implementations perform slightly better than others, all of them exhibit very good size control and high power, even in relatively small samples. An application to a comprehensive data set of sea surface temperatures further illustrates the usefulness of the test. (C) 2020 Elsevier Inc. All rights reserved.
【 授权许可】
Free
【 预 览 】
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