ON BALANCED HALF-SAMPLE VARIANCE-ESTIMATION IN STRATIFIED RANDOM SAMPLING

Establishment surveys based on list frames often use stratified random sampling with a small number of strata, H, and relatively large sampl e sizes, n(h), within strata. For such surveys, a grouped balanced hal f-sample (GBHS) method is often used for variance estimation and for c onstruction of confidence intervals on population parameters of intere st. In this method the sample in each stratum is first randomly divide d into two groups,and then the balanced half-sample (BHS) method is ap plied to the groups. We show that the GBHS method leads to asymptotica lly incorrect inferences as the strata sample sizes n(h) --> infinity with H fixed. To overcome this difficulty, we propose a repeatedly gro uped balanced half-sample (RGBHS) method, which essentially involves i ndependently repeating the grouping T times and then taking the averag e of the resulting T GBHS variance estimators. This method retains the simplicity of the GBHS method. We establish its asymptotic validity a s min n(h) --> infinity and T --> infinity. We also study an alternati ve method by forming substrata within each stratum, consisting of a pa ir of sampling units, and then applying the BHS method on the total se t of substrata, treating them as strata. We establish its asymptotic v alidity as min n(h) --> infinity. We provide simulation results on the finite-sample properties of the GBHS, RGBHS, the jackknife, and the a lternative BHS method. Our results indicate that the proposed RGBHS me thod 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.