Salvati, Nicola; Chandra, Hukum; and Chambers, Ray, Model Based Direct Estimation of Small Area Distributions, Centre for Statistical and Survey Methodology, University of Wollongong, Working Paper 20-10, 2010, 28p.
Much of the small area estimation literature focuses on population totals and means. However, users of survey data are often interested in the finite population distribution of a survey variable, and the measures (e.g. medians, quartiles, percentiles) that characterise the shape of this distribution at small area level. In this paper we propose a model-based direct estimator (MBDE, see Chandra and Chambers, 2009) of the small area distribution function. The MBDE is defined as weighted sum of sample data from the area of interest, with weights derived from the calibrated spline-based estimate of the finite population distribution function introduced by Harms and Duchesne (2006), under an appropriately specified regression model with random area effects. We also discuss the mean squared error estimation of the MBDE. Monte Carlo simulations based on both simulated and real datasets show that the proposed MBDE and its associated mean squared error estimator perform well when compared with alternative estimators of the area-specific finite population distribution function.