Wilmer Prentius | Searcharxiv

arXiv2026

Distributionally balanced sampling designs via minimum tactical configurations

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.

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arXiv2026

Distributionally balanced sampling designs

We propose Distributionally Balanced Designs (DBD), a new class of probability sampling designs that target representativeness at the level of the full auxiliary distribution rather than selected moments. In disciplines such as ecology, forestry, and environmental sciences, where field data collection is expensive, maximizing the information extracted from a limited sample is critical. More precisely, DBD can be viewed as minimum discrepancy designs that minimize the expected discrepancy between the sample and population auxiliary distributions. The key idea is to construct samples whose empirical auxiliary distribution closely matches that of the population. We present a first implementation of DBD based on an optimized circular ordering of the population, combined with random selection of a contiguous block of units. The ordering is chosen to minimize the design-expected energy distance, a discrepancy measure that captures differences between distributions beyond low-order moments. This criterion promotes strong spatial spread, and yields low variance for Horvitz-Thompson estimators of totals of functions that vary smoothly with respect to auxiliaries. Simulation results show that approximate DBD achieves better distributional fit than state-of-the-art methods such as the local pivotal and local cube designs. Hence, DBD can improve the reliability of estimates from costly field data, making distributional balancing effective for constructing representative surveys in resource-constrained applications.

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