Applied Analysis Of Small Area Estimators In Complex Sampling

Objectives The purpose of the study is to introduce some design-based and mode-based estimators of small area, to exame the performance of different types of small area estimators through a well-designed simulation study, based on the NHBSS, as well as the NHBSS example data analysis, and to provide methodological references for effective analysis of small area data in similar complex sampling.Methods A review of some important design-based and model-based small area estimators was given. Only total persons in age-sex groups can be obtained at the national level by the NHBSS, so design-based indirect estimators such as count-synthetic estimator, composite estimator and sample size dependent (SSD) estimator were considered. The variables of interest were binary, the Hierarchical Bayes (HB) estimator was also considered. The expansion estimator is design-based unbiased. A Monte Carlo simulation experiment based on NHBSS was conducted, with replication samples R=500. Average absolute relative bias (AARB) measures bias, while average relative mean squared error (ARMSE) measures accuracy. The performance of five different types of estimators was examed. Relative bias (RB), relative standard error (RSE) and relative root mean squared error (RRMSE) were used to evaluate the reliability of five types of estimators in NHBSS example data analysis. Results Under the context of simulation, whether HBsAg or Anti-HBs in age group 1～59, HB estimator was most biased, but most stable and reliable. There was little defference between expansin estimator, synthetic estimator, composite estimator and SSD estimator for bias or accuracy. These estimators were less biased and more unstable than HB estimator. Overall, the performance of composite estimator was best. In addition, the samller the parameters estimated were, the larger the bias and the less the accuracy were for five types of estimators. Except for in 1～4 age group, the ARMSE of HB estimator for HBsAg among other age groups were smallest. Similar to the results in age group 1～59, HB estimator was most biased among other age groups. There was little diference among other estimators for anti-HBs in bias or accuracy. Overall, the performance of composite estimator was best. Moreover, the bias and accuracy of estimators correlated to the expected sample size and the parameters estimated. The smaller the expected sample size and the parameters estimated were, the more biased and the less stable the esimators were. The bias was smallest and the accuracy was largest for five estimators in age group 1～59. while vice versa in age group 5～14. Under the context of NHBSS example data analysis, whether HBsAg or anti-HBs, the Av.RRMSE of composite estimator was smallest in all age groups, showing that the composite estimator was most stable and reliable, followed by SSD estimator and synthetic estimator. The Av.RRMSE of HB estimator for HBsAg in age group 1～4 and 5～14, as well as for anti-HBs in age group 1～4 was samller than that of expansion estimator, showing that the reliability of HB estimator was prior to that of expansion estimator if the sample size or the parameter was small. Under this scenario, the expansin estimator was most unreliable, such as the Av.RRMSE of expansion estimator for HBsAg in age group 1～4 and 5～14 was 56% and 40.46% respectively.Conclusions Although the results of this study can not bring a breakthrough in the study of small area estimation, further analysis or second analysis of large scale survey data can be facilitated by them. By using the total persons in age-sex groups at the natinal level, composite estimator was more stable and reliable than other estimators for NHBSS data, followed by SSD estimator. The results of HB estimator can not be satisfied, for the reason that the model was not adequate. More parameters or effects will be included in the model in future studies to improve the estimation and decrease the MSE of estimator. Under the context of the expected sample size and the parameters estimated were small, expansion estimator was most unstable and should be avoided to apply; while it can be used under the scenario of the parameters estimated were large, or the sample size was moderate or large.