Selection of sampling units under a correlated population based on the eigensystem of the population covariance matrix

For the prediction problem in survey sampling under a finite population, n sampling units are selected out of N population units and observed to predict the population quantity of interest. For a correlated spatial population, one can obtain lower prediction mean-square error with careful sampling arrangement of the sampling sites. For example, a systematic design can be used to select samples for better prediction results. However, it is only effective under certain population covariance structures. For more general cases, the optimal sampling strategies proposed by different authors in the past can be used to select the optimal sample with which the mean-square error can be minimized. Nevertheless, the computational load can be very intensive, and also the optimization algorithm used is not easy to implement. In addition, the exact population distribution has to be assumed. Two sampling methods, that are based on the eigensystem of the population covariance matrix, are proposed in this article. These sampling methods require fewer population assumptions and the sampling procedures are straightforward. No computationally intensive algorithm is required. Simulation study shows that they can be more efficient than simple random sampling. An example on the utilization of the proposed sampling methods in practice is also presented.