A simple bootstrap method for large entropy unequal probability sampling designs

We propose a simple bootstrap method for large entropy unequal probability sampling designs for finite populations. The method belongs to the class of bootstrap techniques that generate replication weights directly for the sampled units. It produces integer replication weights and is applicable to both equal and unequal probability designs characterized by high entropy, such as randomized systematic, pivotal, and maximum entropy designs. Our approach relies on the Dirichlet-Multinomial distribution to generate bootstrap samples while ensuring desirable statistical properties. We provide an efficient implementation in R and validate the method through simulations using real-world data. Results show that the proposed bootstrap estimator performs comparably to established variance estimation techniques while offering greater flexibility for non-linear estimators.