Small Area Quantile Estimation

October 28, 2015, 2:00pm
Location: Department of Mathematics and Statistics, York University, Toronto, ON
Room: N638 Ross
Speaker: Jiahua Chen, University of British Columbia

Abstract: Sample surveys are widely used to obtain information about totals, means, medians and other parameters of finite populations. In many applications, similar information is also desired on sub-populations such as individuals in specific geographic areas and socio-demographic groups. Often, the surveys are conducted at national or similarly high levels. The random nature of the probability sampling can result in few sampling units from many unplanned sub-populations at the design stage. Estimating parameters of these sub-populations (small areas) with satisfactory precision and evaluating their accuracy pose serious challenges to statisticians. Short of direct information, statisticians resort to pooling information across small areas via suitable model assumptions and administrative archives and census data. In this paper, we propose three estimators of small area quantiles for populations admitting a linear structure with normal error distributions or error distributions satisfying a semi-parametric density ratio model (DRM). We studies the asymptotic properties of the DRM-based method and find it root-n consistent. Extensive simulation studies are used to reveal properties of three methods under various foreseeable populations. The DRM-based is found significantly more efficient when the error distribution is skewed and has comparable efficiency with other methods in other cases.

This talk is sponsored by the CANSSI CRT Project “Statistical Inference for Complex Surveys with Missing Observations”.

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