**4.2.5 Kriging and cokriging neighborhood**

Quite often, the amount of available data is large and using all of the available data is impractical and a selection of the most relevant data is required. One therefore defines a local window or "kriging neighborhood" in which to search for nearby data and to perform local estimation. The shape of the neighborhood should explicitly consider the detected anisotropies, by making the search radius dependent on the variogram range: the larger the range along a direction, the larger the search radius. Typically, the neighborhood is defined by placing an ellipse around the target location, and selecting a given number of data within this ellipse. The justification for such a practice is the so-termed screening effect, according to which the closest data screen out the influence of farthest data (David, 1976; Stein, 2002). Also, to avoid the selection of clustered data that convey redundant information, it is good practice to divide the neighborhood into several angular sectors (e.g., quadrants or octants) and to look for data within each sector (Isaaks and Srivastava, 1989).

Such a definition of the kriging neighborhood is, however, mainly heuristic and one is usually not aware of which data are really worth being included in the neighborhood, and which data can be discarded without deteriorating the estimation. The optimal neighborhood actually depends on the variogram of the variable of interest, as the screening effect does not occur with every variogram model. Some generic guidelines have been provided by Rivoirard (1987) to validate the choice of a given neighborhood in the univariate context.

In the multivariate case, the design of the neighborhood is more complex and critical. For instance, the data of a covariate may be screened out by the collocated data of the primary variable or, on the contrary, they may supplement the primary data and provide useful information to improve local estimation. As suggested by recent publications (Rivoirard, 2004; Subramanyam and Pandalai, 2008), the decision to include or not the covariate data should consider the correlation structure of the coregionalized variables and the sampling scheme (in particular, whether or not all the variables are measured at all the sampling locations). Some options include:

