Distributionally balanced sampling designs

TL;DR

This paper introduces Distributionally Balanced Designs (DBD), a novel sampling method that improves representativeness by matching the auxiliary distribution of the sample to that of the population, enhancing estimate reliability in resource-limited data collection.

Contribution

The paper presents a new class of sampling designs that focus on distributional matching rather than moment matching, with an implementation based on optimized circular ordering and discrepancy minimization.

Findings

DBD achieves better distributional fit than existing methods.

It reduces variance for estimators of smoothly varying functions.

Simulation results demonstrate improved reliability in resource-constrained surveys.

Abstract

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.