UBC Theses and Dissertations
Small area quantile estimation under unit-level models Zhang, Qiong
Sample surveys are widely used as a cost-effective way to collect information on variables of interest in target populations. In applications, we are generally interested in parameters such as population means, totals, and quantiles. Similar parameters for subpopulations or areas, formed by geographic areas and socio-demographic groups, are also of interest in applications. However, the sample size might be small or even zero in subpopulations due to the probability sampling and the budget limitation. There has been intensive research on how to produce reliable estimates for characteristics of interest for subpopulations for which the sample size is small or even zero. We call this line of research Small Area Estimation (SAE). In this thesis, we study the performance of a number of small area quantile estimators based on a popular unit-level model and its variations. When a finite population can be regarded as a sample from some model, we may use the whole sample from the finite population to determine the model structure with a good precision. The information can then be used to produce more reliable estimates for small areas. However, if the model assumption is wrong, the resulting estimates can be misleading and their mean squared errors can be underestimated. Therefore, it is critical to check the robustness of estimators under various model mis-specification scenarios. In this thesis, we first conduct simulation studies to investigate the performance of three small area quantile estimators in the literature. They are found not to be very robust in some likely situations. Based on these observations, we propose an approach to obtain more robust small area quantile estimators. Simulation results show that the proposed new methods have superior performance either when the error distribution in the model is non-normal or the data set contain many outliers.
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