Estimating and testing zones of abrupt change for spatial data

We propose a method for detecting (i.e. estimating and testing) the zones where a variable irregularly sampled in the plane changes abruptly. Under the null hypothesis the variable of interest is the realisation of a stationary Gaussian process with constant expectation. The alternative is that the mean function presents abrupt changes. Local test statistics are first built using distribution properties of the estimated gradient under the null hypothesis. The points where the local test statistics is above a determined threshold define potential Zones of Abrupt Change (ZACs). We then design a global test to assess the global significance of the potential ZACs. The theory that links the threshold and the global level is based on the asymptotic distribution of excursion sets of nonstationary χ2 fields for which new results are established. Issues arising when implementing the method are discussed and the method is evaluated by a simulation study. Its application to a soil data set from an agricultural field shows how it can be used in an exploratory analysis for proposing a subdivision of the domain.