Comparison of statistical methods for testing the hypothesis of constant global mean in spatial statistics

In spatial statistics in general, and in geostatistics in particular, the choice between a spatial model with drift and a model with constant global mean is often critical, especially when only a small number of samples are available. A statistical test provides an objective means of making this choice. Among the many available statistical tests, a variance-ratio test has been widely used for making this choice because of its good statistical properties but, in addition to a semi-variogram model, it also requires an alternative drift model hypothesis. Another test statistic is the global D-statistic, which is a complementary test in the sense that it does not require an alternative hypothesis model. In this paper, we use sparse data from simulated random fields to evaluate and compare the performances of these two methods for testing the hypothesis of constant global mean in spatial statistics. We do so by considering the influence of four factors: the amount of data, the type of random field, the amount of spatial or temporal correlation and parametric drifts. In addition, we evaluate their performances in time series analysis, in which testing the hypothesis of constant global mean is also of significant interest. The two test statistics are compared in terms of their achieved confidence level and achieved power. The better method is the one that achieves the nominal confidence level and has higher power. We discuss departures from the nominal values and the results are used to highlight the importance of this problem in spatial statistics.