Competitors to genuine \pi ps sample designs: A comparison - ARCHIVED

Without-replacement list sampling with probability proportional to some measure of element size has not enjoyed much application in forestry because of the difficulty of implementing such sample strategies, that have been termed \pi ps designs to distinguish without-replacement sampling from the well-known with-replacement pps designs. In this contribution, an exact \pi ps strategy (Sunter’s variant 2), an approximate \pi ps design (Sunter’s variant 1) and the Rao-Hartley-Cochran random group method are examined and the variances of the respective estimators for total bole volume are computed for four tree populations. The results indicate that compared to the Rao-Hartley-Cochran design Sunter’s variant 1 in general leads to higher precision if the relationship between auxiliary information x_k and target characteristic y_k is loose but is sensitive to the ordering of the sampling frame, whereas the Rao-Hartley-Cochran design does not require the sampling frame to be ordered at all and appears to be superior if strong linear relationships between x_k and y_k are present.