Successive forest inventories using multistage sampling with partial replacement of units
Creators: name: Omule, Stephen Agnew Yen’Emurwon
Publisher: name: University of British Columbia
Year: 2010

description: Effective sampling methods for successive forest inventories include versions of multistage sampling. Multistage sampling, or subsampling, is cost-effective in broad forest areas, and it is one technique that lends itself advantageously to the use of 'multilevel data. Improved efficiency of sampling designs for successive inventories is usually achieved through partial replacement of sampling units at the successive occasions. However, the theory on multistage sampling on successive occasions with partial replacement of units has some limitations. All of the theory invokes the distinctive assumptions of equal sample size or equal variance on successive occasions. These assumptions are not usually met in forestry. The objective of this study was to provide some general theory for successive forest inventories using multistage sampling with partial replacement of units. As is the case with multistage designs, the technique of partial replacement gives rise to a number of alternatives. For practical purposes, only the case in which partial replacement occurs at the primary stage of the multistage design was considered. In addition, consideration was restricted to inventories on two successive occasions only, without the restrictive assumptions of equal sample size or equal variance at the two occasions. Minimum-variance (best) linear and unbiased estimators (BLUE) of the current population mean μ[sub γ] and of the change in the mean between two successive occasions A, together with their respective variances are derived for two-stage, three-stage, and h-stage (h &gt; 1) designs. Biased estimators of the ratio form (RE) of μ[sub γ] and of Δ are also derived together with their respective variances and biases, for a two-stage design. The biases of REs are negligible for large sample sizes. A numerical comparison of the efficiency of BLUE and RE for estimating μ[sub γ] indicated that the BLUE had a slight edge over the RE; however, for estimating Δ, the RE was very inefficient. An alternative solution approach is proposed for the problem of determining the optimum' replacement policy, that is, the number of primary units to remeasure and new ones to take at the current occasion. The sequential nature of successive inventories is exploited to cast the problem as a multistage process that can be optimized through dynamic programming. Solution procedures are given for determining the optimum replacement policy for a two-stage design with the objective of minimizing the cost of the inventory and subject to the side conditions that the specified variance levels of μ[sub γ] and Δ are met. The derived theory was illustrated, for a two-stage design, by working through a sample forest inventory problem. From a practical point of view, extension of the theory of sampling with partial replacement from one-stage to multistage designs is beneficial, particularly for the inventory of large forest areas. It would be useful to extend the theory further to use variable probabilities of selection at the various stages of the multistage design; and to examine the cases in which partial replacement occurs at other than the primary stage.