Small-Area Quantile Estimation

• Activity Number: 347
• Type: Topic Contributed
• Date/Time: Tuesday, August 11, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Jiahua Chen* and Yukun Liu
• Companies: The University of British Columbia and East China Normal University
• Keywords: Empirical likelihood ; Density ratio model ; Finite population ; Sampling survey

Abstract

Sample surveys are widely used to obtain information about totals, means 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 sub-populations of interest. Estimating parameters of these sub-populations 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. Most existing discussions have focused on estimating small area means under models geared to various scenarios. These models would be overstretched if used for estimating small area quantiles. In this paper, we postulate that the small area population distributions contain a linear structure with error distributions satisfying a density ratio model. Under this model, we employ empirical likelihood to pool information in samples across all small areas. The resulti