Small Area Estimation with Spatially Varying Natural Exponential Families

TL;DR

This paper introduces a spatially varying natural exponential family model for small area estimation, employing geographically weighted regression to improve efficiency over traditional models in the presence of spatial heterogeneity.

Contribution

It proposes a novel two-stage area-level model with spatially varying parameters and a new empirical Bayes estimator, addressing limitations of exchangeable models.

Findings

The proposed method outperforms traditional models in simulations.

It effectively estimates in non-sampled areas.

Application to real data demonstrates improved accuracy.

Abstract

Two-stage hierarchical models have been widely used in small area estimation to produce indirect estimates of areal means. When the areas are treated exchangeably and the model parameters are assumed to be the same over all areas, we might lose the efficiency in the presence of spatial heterogeneity. To overcome this problem, we consider a two-stage area-level model based on natural exponential family with spatially varying model parameters. We employ geographically weighted regression approach to estimating the varying parameters and suggest a new empirical Bayes estimator of the areal mean. We also discuss some related problems, including the mean squared error estimation, benchmarked estimation, and estimation in non-sampled areas. The performance of the proposed method is evaluated through simulations and applications to two data sets.