On Balanced Half-Sample Variance Estimation in Stratified Random Sampling

Abstract

Establishment surveys based on list frames often use stratified random sampling with a small number of strata, H, and relatively large sample sizes, n_h, within strata. For such surveys, a grouped balanced half-sample (GBHS) method is often used for variance estimation and for construction of confidence intervals on population parameters of interest. In this method the sample in each stratum is first randomly divided into two groups, and then the balanced half-sample (BHS) method is applied to the groups. We show that the GBHS method leads to asymptotically incorrect inferences as the strata sample sizes n_h \rightarrow \infty with H fixed. To overcome this difficulty, we propose a repeatedly grouped balanced half-sample (RGBHS) method, which essentially involves independently repeating the grouping T times and then taking the average of the resulting T GBHS variance estimators. This method retains the simplicity of the GBHS method. We establish its asymptotic validity as \min n_h \rightarrow \infty and T \rightarrow \infty. We also study an alternative method by forming substrata within each stratum, consisting of a pair of sampling units, and then applying the BHS method on the total set of substrata, treating them as strata. We establish its asymptotic validity as \min n_h \rightarrow \infty. We provide simulation results on the finite-sample properties of the GBHS, RGBHS, the jackknife, and the alternative BHS method. Our results indicate that the proposed RGBHS method performs well for T as small as 15, thus providing flexibility in terms of the number of half-samples used. The alternative BHS method has also performed well in the simulation study.