Small area estimation with subgroup analysis

ABSTRACT

In this article, a new unit level model based on a pairwise penalised regression approach is proposed for problems in small area estimation (SAE). Instead of assuming common regression coefficients for all small domains in the traditional model, the new estimator is based on a subgroup regression model which allows different regression coefficients in different groups. The alternating direction method of multipliers (ADMM) algorithm is used to find subgroups with different regression coefficients. We also consider pairwise spatial weights for spatial areal data. In the simulation study, we compare the performances of the new estimator with the traditional small area estimator. We also apply the new estimator to urban area estimation using data from the National Resources Inventory survey in Iowa.

KEYWORDS:

• Linear mixed models
• penalty regressions
• small area estimation
• spatial areal data
• subgroup analysis

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported in part by the Natural Resources Conservation Service of the U.S. Department of Agriculture.

Notes on contributors

Xin Wang

Xin Wang is currently an Assistant professor in Department of Statistics at Miami University. Her research interests are spatial data analysis, Bayesian statistics, clustering, convergence rates of MCMC algorithms and survey sampling.

Zhengyuan Zhu

Zhengyuan Zhu is currently a Professor in Department of Statistics at Iowa State University, director of Center for Survey Statistics & Methodology. His research interests include spatial statistics, survey statistics, time series analysis, and multivariate analysis.