Salvati, N.; Tzavidis, N.; Pratesi, M.; and Chambers, R., Small Area Estimation Via M-quantile Geographically Weighted Regression, Centre for Statistical and Survey Methodology, University of Wollongong, Working Paper 09-09, 2009, 30p.
One popular approach to small area estimation when data are spatially correlated is to employ Simultaneous Autoregressive (SAR) random effects models to define the Spatial Empirical Best Linear Unbiased Predictor (SEBLUP). See Singh et al. (2005) and Pratesi and Salvati (2008). SAR models allow for spatial correlation in the error structure. An alternative approach that incorporates the spatial information in the regression model is to use Geographically Weighted Regression (GWR). See Brunsdon et al. (1996) and Fotheringham et al. (1997). GWR extends the traditional regression model by characterising the relationship between the outcome variable and the covariates via local rather than global parameters. In this paper we investigate GWR-based small area estimation under the M-quantile modelling approach (Chambers and Tzavidis, 2006). In particular, we integrate the concepts of outlier-robust small area estimation and borrowing strength over space within a unified modelling framework by specifying an M-quantile GWR model that is a local model for the M-quantiles of the conditional distribution of the outcome variable given the covariates. This model is then used to define an outlier-robust predictor of the small area characteristic of interest that also accounts for spatial association in the data. An additional important spin-off from applying the M-quantile GWR small area model is more efficient synthetic estimation for out of sample areas. We demonstrate the usefulness of this framework through both model-based as well as design-based simulation, with the latter based on a realistic survey data set. The paper concludes with an application to environmental data for predicting average levels of the Acid Neutralizing Capacity at 8-digit Hydrologic Unit Code level in the Northeast states of the U.S.A.