Balanced Sampling With Inequalities: Application to Category Bounding, Matrix Rounding, and Spread Sampling

• 成果类型: Article; Early Access
• 署名作者: Tripet, Arnaud; Tille, Yves
• 署名单位: University of Neuchatel
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2025.2550667
• 发表日期: 2025
• 关键词: variance-estimation; corrado gini; approximation; probabilities

摘要

In this article, we propose a novel algorithm for balanced sample selection with linear inequality constraints, ensuring that estimators remain within fixed bounds. This algorithm extends the cube method of Deville and Till & eacute;, allowing the selection of a sample from a database where Horvitz-Thompson estimators of totals are equal or nearly equal to the true population totals. The new algorithm has several key applications, including imposing minimum sample sizes for small areas and constraining sample sizes in potentially overlapping categories. It also addresses the controlled rounding matrix problem and links to systematic sampling with unequal probabilities. It can also be used to select doubly stratified samples when the sums of the inclusion probabilities in the strata are not integer. Additionally, the algorithm enables the selection of spatially spread samples. Simulations demonstrate that this new method performs comparably to other spread sampling techniques. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.