Detecting the optimal sample size in adaptive sampling design

The adaptive cluster sampling is a suitable sampling design useful to estimate the parameters of a biological population that results to be clustered and spread over a very large area. One of the relevant drawbacks of this sampling design is related to the uncertainty of the final sampling fraction. In particular, when sampling is very expensive or when there are logistical constraints, the extra sampling effort may outweigh the loss of efficiency and the conventional designs may be preferable. In this framework Restricted Adaptive Cluster Sampling was proposed in which a limit is placed on the sample size prior to sampling. However, in this procedure there are several unsolved inferential problems. In this paper a test, able to detect the optimal sample size, is developed. The methodology proposed is based on the use of the bootstrap and the replicated sampling design. The empirical distribution of the difference between two abundance estimators in two steps is obtained. Furthermore, the stop criterion on adaptive sampling is established by means a suitable test of hypothesis.