Inference From Stratified Samples: Properties of the Linearization, Jackknife and Balanced Repeated Replication Methods

Abstract

The asymptotic normality of both linear and nonlinear statistics and the consistency of the variance estimators obtained using the linearization, jackknife and balanced repeated replication (BRR) methods in stratified samples are established. The results are obtained as $L \rightarrow \infty$ within the context of a sequence of finite populations $\{\Pi_L\}$ with $L$ strata in $\Pi_L$ and are valid for any stratified multistage design in which the primary sampling units (psu's) are selected with replacement and in which independent subsamples are taken within those psu's selected more than once. In addition, some exact analytical results on the bias and stability of these alternative variance estimators in the case of ratio estimation are obtained for small $L$ under a general linear regression model.