A Stopping Rule for Simulation‑Based Estimation of Inclusion Probabilities

Design‑based estimation of finite population parameters such as totals usually relies on the knowledge of inclusion probabilities characterising the sampling design. They are directly incorporated into sampling weights and estimators. However, for some useful sampling designs, these probabilities may remain unknown. In such a case, they may often be estimated in a simulation experiment which is carried out by repeatedly generating samples using the same sampling scheme and counting occurrences of individual units. By replacing unknown inclusion probabilities with such estimates, design‑based population total estimates may be computed. The calculation of required sample replication numbers remains an important challenge in such an approach. In this paper, a new procedure is proposed that might lead to the reduction in computational complexity of simulations.