Small area estimation with spatially varying natural exponential families

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.

Keywords:

• Empirical Bayes estimation
• geographically weighted regression
• mean squared error
• natural exponential family with quadratic variance function
• small area estimation

2010 Mathematics Subject Classification:

• 62C12

Acknowledgments

We are thankful to Tatsuya Kubokawa and Hisashi Noma for their valuable comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Japan Society for the Promotion of Science (KAKENHI) Grant Numbers JP18K12757, JP19K13667 and JP16K17153.