Spatial Data and Kriging.
If Yi is an observation taken at some point in space, then x~ consists of the coordinates of the point, or, more generally, some function of the coordinates. In dealing with spatial data, finding the BLUP is generally called Kriging. The real challenge with spatial data is getting some idea of the covariance matrices V and Vyo. See Christensen (2001) for a more detailed discussion with additional references.