Hierarchical Bayes estimation of small area means under a spatial nonstationary Fay-Herriot model

The Fay-Herriot (FH) model is widely used in small area estimation (SAE) for aggregated level data, but in several applications presence of spatial effect between contiguous or neighboring region cannot be denied which is not handled by this model. Conditional Autoregressive and Simultaneous Autoregressive specifications do incorporate spatial associationship while taking into account the spatial correlation effects among areas. However, none of these approaches implement the idea of spatially varying covariates through spatially dependent fixed effect parameters. Such approach in statistics is known as spatial nonstationarity. This article introduces spatial nonstationary version of FH model considering hierarchical Bayesian paradigm and then deliberates estimation of small area means. The proposed SAE approach is evaluated through extensive simulation studies. The empirical results from simulation studies demonstrate the superiority of proposed spatial nonstationary SAE method over the nonspatial and stationary alternatives. The method is also applied to estimate paddy (green) crop yield at district level in the state of Uttar Pradesh in India using survey data from the improvement of crop statistics scheme and linked with Census data. A spatial map presents a quick view to the regional variations or disparity in district level yield estimates and are certainly helpful to the decision makers for identifying the regions and areas requiring more attention for designing targeted interventions and policy development.