Testing for constant spatial mean using the global D-statistic

Abstract

The authors introduce the D-statistic for testing for a constant spatial mean in geostatistical applications, i.e. testing for the presence or absence of a global drift. The D-statistic can be calculated with sparse data and for different directions and a statistical test of hypothesis of constant spatial mean has been designed using the global standardized D-statistic. If, for a given data set, the null hypothesis of constant mean cannot be accepted, a model with a (non-constant) drift would be more appropriate. The estimated confidence level and estimated power of the D-statistic hypothesis test is studied using Monte Carlo simulation, with different assumptions about the random field, the drift, the scale of variability of the drift and the number of experimental data (i.e. sample size). Case studies are provided to illustrate the application and interpretation of the results. The Fortran computer program D2STAT2D is provided for calculating the standardized global D-statistic from sparse data in the plane.