🤖 AI Summary
This work proposes a novel sampling design based on minimal tactical configurations to overcome the limitations of existing spatially balanced sampling methods, which rely on cyclic sequences and enforce contiguous sample blocks, thereby restricting design flexibility. By eliminating topological constraints on sample contiguity, the proposed approach expands the feasible design space while maintaining fixed sample size and equal inclusion probabilities. An initialization strategy that accommodates arbitrary sample sizes and incorporates spatial awareness, combined with simulated annealing optimization, effectively reduces expected bias. Experimental results demonstrate that the method outperforms state-of-the-art techniques in terms of distributional fidelity, variable balance, and spatial dispersion, achieving both theoretical optimality and practical superiority.
📝 Abstract
Distributionally balanced sampling designs are low-discrepancy probability designs obtained by minimizing the expected discrepancy between the auxiliary-variable distribution of a random sample and the target population distribution. Existing constructions rely on circular population sequences, which restrict the design space by forcing samples to be contiguous blocks of a sequence. We propose a new construction based on minimum tactical configurations that removes this topological constraint. The resulting designs are fixed-size, have equal inclusion probabilities, and belong to the class with minimum feasible configuration size. We develop both a simple initialization valid for arbitrary population and sample sizes and a spatial initialization that yields a lower initial expected discrepancy, together with a simulated annealing algorithm for optimization within this class. In simulations and empirical examples, the proposed method outperforms state-of-the-art alternatives in terms of distributional fit, balance, and spatial spread.