Small Area Estimation under Density Ratio Model

Sample surveys are widely used to obtain information about totals, means and other parameters of finite populations. In many applications, the same information are also desired for subpopulations 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 no 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. Lacking sufficient amount of direction information, statisticians resort to suitable models to pool the information across small areas. Most existing discussions have focused on estimating small area means under some models corresponding to imaginary scenarios. They are likely less effective if utilized for estimating small area quantiles. In this paper, we postulate that the small area population distributions have some linear structure with error distributions satisfying a density ratio model. That is, the small area error distributions are all tilted distributions from a common basis. Under this model, we employ empirical likelihood to pool information in samples across all small areas. The resulting approach not only allows us to estimate small area means, but also small area quantiles. We give a comprehensive discussion on this method and provide some preliminary simulation results to illustrate its potential. Key Words: Empirical best linear unbiased predictors, empirical likelihood, nested error model, population quantile, survey sampling. 1