Revisiting the random shift approach for testing in spatial statistics

Kód výsledku v 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>

Nalezeny alternativní kódy

RIV/00216208:11320/21:10434480

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Revisiting the random shift approach for testing in spatial statistics

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Revisiting the random shift approach for testing in spatial statistics

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10103 - Statistics and probability

Projekt

<a href="/cs/project/GA19-04412S" target="_blank" >GA19-04412S: Nové přístupy k modelování a statistice náhodných množin</a><br>

Návaznosti

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

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název periodika

Spatial Statistics

ISSN

2211-6753

e-ISSN

—

Svazek periodika

2021

Číslo periodika v rámci svazku

42

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

17

Strana od-do

1-17

Kód UT WoS článku

000635279000007

EID výsledku v databázi Scopus

2-s2.0-85080869183