Numerical Comparison Between Different Empirical Prediction Intervals Under the Fay-Herriot Model

Abstract

Recently, an empirical best linear unbiased predictor is widely used as a practical approach to small area inference. It is also of interest to construct empirical prediction intervals. However, we do not know which method should be used from among the several existing prediction intervals. In this article, we first obtain an empirical prediction interval by using the residual maximum likelihood method for estimating unknown model variance parameters. Then we compare the later with other intervals with the residual maximum likelihood method. Additionally, some different parametric bootstrap methods for constructing empirical prediction intervals are also compared in a simulation study.

Keywords:

• Empirical best linear unbiased prediction
• Empirical prediction interval
• Residual maximum likelihood method
• Small area estimation

Mathematics Subject Classification:

• Primary 62F25
• Secondary 62J05

Additional information

Funding

This work was supported by JSPS KAKENHI Ggrant Nnumber 242742.