TThis paper develops a Dynamic Mini-Max (DMM) framework for repeated surveys comprising a Dynamic Mini-Max Design and a Sequential Hierarchical Bayes Update (SHBU). The DMM jointly optimizes sample size and wave overlap subject to simultaneous precision constraints for levels and movements, a respondent burden limit, and a fieldwork budget. The methods are illustrated using 2021 Australian Census data (t = 1) and simulated waves t = 2, 3, 4. Both the DMM and the classical design start from the same 5% proportional allocation of n_A = 42,018 units. The DMM reduces this to n* = 40,251 while meeting all precision constraints, achieving a cost saving of approximately 6.3%. Level coverage is comparable between the two designs (maximum absolute relative error (MARE) ratio 0.844--1.263). Movement coverage diverges markedly: the DMM achieves 100% across all 27 domain-variable cells, while the classical design achieves only 82%--96% (87.5%--95.0% nationally). The classical confidence interval understates movement uncertainty because it addresses sampling variance only and does not account for the model variance component V_mod_hat. Additional benefits of the DMM framework -- including coherent joint inference for levels and movements, sequential updating without ad hoc composite-estimator chaining, and small area estimation -- are outlined in the paper.

翻译：本文针对重复调查构建了动态极小极大(DMM)框架，包含动态极小极大设计与序贯分层贝叶斯更新(SHBU)两部分。DMM方法在同时满足水平量与变化量的精度约束、受访者负担限制及实地调查预算的前提下，联合优化样本规模与波次重叠。方法基于2021年澳大利亚人口普查数据(t=1)及模拟波次(t=2,3,4)进行验证。DMM与经典设计均以n_A=42,018个单元的5%比例分配为起点。DMM在满足所有精度约束的条件下将样本量缩减至n*=40,251，实现约6.3%的成本节省。两种设计的水平覆盖度相当（最大绝对相对误差比值0.844-1.263）。变化量覆盖度呈现显著差异：DMM在全部27个域-变量单元格中实现100%覆盖，而经典设计的全国覆盖率仅为82%-96%（国家级87.5%-95.0%）。经典置信区间低估了变化量不确定性，因其仅考虑抽样方差而未纳入模型方差分量V_mod_hat。论文还阐述了DMM框架的附加优势——包括对水平量和变化量进行连贯联合推断、无需临时组合估计链的序贯更新，以及小域估计能力。