Balanced repeated replication (BRR) and the jackknife are two widely used methods for estimating variances in stratified samples with two primary sampling units per stratum. While both methods produce variance estimators that can be expressed as sums of squared stratum-level contrasts, they differ fundamentally in their construction and in the dependence structure of their replicate estimates. This article examines the independence properties of the components contributing to these variance estimators. For BRR, we show that although the replicate estimates themselves are correlated, the balancing property of Hadamard matrices collapses the variance estimator into a sum of independent stratum-specific components. For the jackknife, the independence of components follows directly from the construction. Using these independence results, we derive the variance of each variance estimator and establish a direct connection to the Welch-Satterthwaite degrees of freedom approximation. This yields a practical formula for estimating degrees of freedom when constructing confidence intervals for population totals. The derivation highlights the unified treatment of both replication methods and provides insights into their relative efficiency and applicability.

翻译：平衡重复复制（BRR）与刀切法是两种广泛应用于分层抽样（每层包含两个初级抽样单元）的方差估计方法。尽管这两种方法产生的方差估计量均可表示为层间对比的平方和，但它们在构造方式以及复制估计量的依赖结构上存在根本差异。本文研究了构成这些方差估计量的各分量的独立性特征。对于BRR，我们证明尽管复制估计量本身存在相关性，但哈达玛矩阵的平衡特性使得方差估计量可简化为相互独立的层特异性分量之和。对于刀切法，分量的独立性直接源于其构造方式。基于这些独立性结论，我们推导了各方差估计量的方差，并建立了其与韦尔奇-萨特斯韦特自由度近似之间的直接联系。这为构建总体总量置信区间时估计自由度提供了实用公式。该推导过程凸显了对两种复制方法的统一处理，并深入揭示了它们的相对效率与适用性。