Big Basal Area Factor (Big BAF) and Point-3P are two-stage sampling methods. In the first stage the sampling units, in both methods, are Bitterlich points where the selection of the trees is proportional to their basal area. In the second stage, sampling units are trees which are a subset of the first stage trees. In the Big BAF method, the probability of selecting trees in the second stage is made proportional to the two BAFs' ratio, with a basal area factor larger than that of the first stage. In the Point-3P method the probability of selecting trees, in the second stage, is based on the height prediction and use of a specific random number table. Estimates of the forest stands' volume and their sampling errors are based on the theory of the product of two random variables. The increasing error in the second stage is small, but the total cost of measuring the trees is much smaller than simply using the first stage, with all the trees measured. In general, the two sampling methods are modern and cost-effective approaches that can be applied in forest stand inventories for forest management purposes and are receiving the growing interest of researchers in the current decade.
The Bitterlich Sampling (horizontal point sampling) is a common method in forest inventories. By this method, the Horvitz-Thompson estimator is used in a number of independent sampling points for the estimation of overall tree volume in a forest area/stand. In this paper, confidence intervals are constructed and evaluated using the normal approach and two bootstrap methods; the percentile method (C α ) and the bias-corrected and accelerated method (BC α ). The simulation results show that the normal confidence interval has better coverage of true value at sample size 10. At sample sizes 20 and 30, it seems that there are no substantial differences in coverage between confidence intervals, although it could be noted a small superiority of BC α method. At sample size 40, the coverage of the three confidence intervals is higher than the nominal coverage (95%).
The sampling design is a crucial topic that would be considered in Small Area Estimation (SAE). Applications of sampling designs presented in Forest Inventories (FIs) for SAE, with the two-phase sampling to have the most references. Eventually, FIs that are applied for SAE is an open research topic. An important contribution to this topic would be the comparison and the optimization of sampling designs that aims to improve SAE in FIs.
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