Linear Assignment Sampling: Spatially Balanced Sampling With Auxiliary Variables

Estimating parameters of spatial populations requires a sample of response values distributed over the study region. When spatial trends are present, spatially balanced designs give more precise results for commonly used estimators. If auxiliary variables are available, these can also be included in the design to improve precision further. This article proposes a new spatially balanced design to force sample spread in the space of the auxiliary variables. All we require is a distance measure between population units. Numerical results show that the method generates spatially balanced samples and compares favorably with existing designs. We provide two example applications using spatial populations with auxiliary variables and consider equal and unequal probability designs.