ICAR-Indian Agricultural Statistics Research Institute, New Delhi, India
Abstract: A plug-in empirical predictor under a generalized linear mixed model (GLMM) is often used for small area estimation (SAE) of counts. However, GLMM assumes that the fixed effect parameters are spatially invariant and does not account for the presence of spatial nonstationarity in the data. There are data situations, where this assumption is inappropriate and parameters associated with the model covariates vary spatially. This phenomenon referred to as spatial nonstationarity. A geographically weighted regression extension of the area level version of GLMM is developed, extending this model to allow for spatial nonstationarity, and SAE based on this spatially nonstationary model (NSGLMM) is described. The empirical predictor for small area counts (NSEP) under an area level NSGLMM is proposed. Analytic and bootstrap approaches to estimating the mean squared error of the NSEP are also developed, and a parametric approach to testing for spatial nonstationarity is described. The approach is illustrated by applying it to a study of poverty mapping using socioeconomic survey data from India.