A new generalized confidence interval for the among-group variance in the heteroscedastic one-way random effects model

ABSTRACT

Based on the generalized inference idea, a new kind of generalized confidence intervals is derived for the among-group variance component in the heteroscedastic one-way random effects model. We construct structure equations of all variance components in the model based on their minimal sufficient statistics; meanwhile, the fiducial generalized pivotal quantity (FGPQ) can be obtained through solving an implicit equation of the parameter of interest. Then, the confidence interval is derived naturally from the FGPQ. Simulation results demonstrate that the new procedure performs very well in terms of both empirical coverage probability and average interval length.

KEYWORDS:

• Among-group variance component
• Fiducial generalized pivotal quantity
• Heteroscedastic
• One-way random effects model

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F25

Acknowledgments

We thank the anonymous referee for the valuable suggestions which improved the quality of this article very much.

Funding

Xuhua Liu’s research was supported by the National Natural Science Foundation of China (Grant Nos. 11201478, 11471030, 11471010). Na Li’s research was supported by the National Natural Science Foundation of China (Grant No. 71201160). Yuqin Hu’s work was supported by National Social Science Fund (13CTJ012) and the BCMIIS, the PhD Program Foundation of Ministry of Education of China (20121103110004).