Revisiting the random shift approach for testing in spatial statistics

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60076658%3A12510%2F21%3A43900865" target="_blank" >RIV/60076658:12510/21:43900865 - isvavai.cz</a>

Alternative codes found

RIV/00216208:11320/21:10434480

Result on the web

<a href="https://www.sciencedirect.com/science/article/pii/S2211675320300245?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/pii/S2211675320300245?via%3Dihub</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.spasta.2020.100430" target="_blank" >10.1016/j.spasta.2020.100430</a>

Result language

angličtina

Original language name

Revisiting the random shift approach for testing in spatial statistics

Original language description

We consider the problem of non-parametric testing of independence of two components of a stationary bivariate spatial process. In particular, we revisit the random shift approach that has become the standard method for testing the independent superposition hypothesis in spatial statistics, and it is widely used in a plethora of practical applications. However, this method has a problem of liberality caused by breaking the marginal spatial correlation structure due to the toroidal correction. This indeed means that the assumption of exchangeability, which is essential for the Monte Carlo test to be exact, is not fulfilled. We present a number of permutation strategies and show that the random shift with the variance correction brings a suitable improvement compared to the torus correction in the random field case. It reduces the liberality and achieves the largest power from all investigated variants. To obtain the variance for the variance correction method, several approaches were studied. The best results were achieved, for the sample covariance as the test statistics, with the correction factor . This corresponds to the asymptotic order of the variance of the test statistics.In the point process case, the problem of deviations from exchangeability is far more complex and we propose an alternative strategy based on the mean cross nearest-neighbor distance and torus correction. It reduces the liberality but achieves slightly lower power than the usual cross K-function. Therefore we recommend it, when the point patterns are clustered, where the cross K-function achieves liberality.

Czech name

—

Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10103 - Statistics and probability

Project

<a href="/en/project/GA19-04412S" target="_blank" >GA19-04412S: New approaches to modeling and statistics of random sets</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2021

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Spatial Statistics

ISSN

2211-6753

e-ISSN

—

Volume of the periodical

2021

Issue of the periodical within the volume

42

Country of publishing house

GB - UNITED KINGDOM

Number of pages

17

Pages from-to

1-17

UT code for WoS article

000635279000007

EID of the result in the Scopus database

2-s2.0-85080869183