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A test for stationarity for irregularly spaced spatial data
Author(s) -
Bandyopadhyay Soutir,
Rao Suhasini Subba
Publication year - 2017
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/rssb.12161
Subject(s) - random field , test statistic , statistic , field (mathematics) , mathematics , data set , sampling (signal processing) , representation (politics) , spatial analysis , transformation (genetics) , property (philosophy) , statistics , algorithm , computer science , statistical hypothesis testing , biochemistry , chemistry , philosophy , filter (signal processing) , epistemology , politics , political science , pure mathematics , law , computer vision , gene
Summary The analysis of spatial data is based on a set of assumptions, which in practice need to be checked. A commonly used assumption is that the spatial random field is second‐order stationary. In the paper, a test for spatial stationarity for irregularly sampled data is proposed. The test is based on a transformation of the data (a type of Fourier transform), where the correlations between the transformed data are close to 0 if the random field is second‐order stationary. However, if the random field were second‐order non‐stationary, this property does not hold. Using this property a test for second‐order stationarity is constructed. The test statistic is based on measuring the degree of correlation in the transformed data. The asymptotic sampling properties of the test statistic are derived under both stationarity and non‐stationarity of the random field. These results motivate a graphical tool which allows a visual representation of the non‐stationary features. The method is illustrated with simulations and a real data example.