Small-area estimation under a log-transformed area-level model

ABSTRACT

Area-level models are often used for small-area estimation when auxiliary data are available only as area aggregates. A popular area-level model used for small-area estimation is the Fay–Herriot model. In many small-area applications, the Fay–Herriot model is often fitted on a logarithm (log) scale and model parameters are estimated under this model. This is followed by back-transformation to obtain the estimates for small-area quantities in the original scale. However, back-transformation leads to biased estimates of small-area quantities. This article develops a bias-corrected predictor for small-area quantities under a log-transformed Fay–Herriot model. The empirical results-based simulation studies show that the bias-corrected small-area predictor has both smaller bias and better efficiency as compared to the existing small-area predictors.

KEYWORDS:

• Small area
• log scale
• back-transformation
• bias correction

AMS SUBJECT CLASSIFICATION:

• 62D05

Acknowledgments

The authors acknowledge the valuable comments and suggestions of the associate editor and two anonymous referees. These led to a considerable improvement in the article.