Distributionally balanced sampling designs via minimum tactical configurations

TL;DR

This paper introduces a novel method for creating distributionally balanced sampling designs using minimum tactical configurations, improving flexibility and performance over existing methods.

Contribution

It removes topological constraints in sampling design construction by leveraging tactical configurations, enabling more flexible and optimal distributional properties.

Findings

Outperforms existing methods in distributional fit and balance

Provides a flexible construction avoiding circular sequence restrictions

Demonstrates improved spatial spread in empirical examples

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.