Confidence Intervals for Linear Function of Variance Components in Two-Fold Nested Random Effects Model

Abstract

In the article, we consider the unbalanced case of the two-way nested random effects model under partial balance. Using the method of generalized confidence intervals (GCIs) introduced in Weeranhandi (1993 1995), a new method is proposed for constructing confidence intervals on linear function of variance components. To compare the resulted intervals with the Modified Large Sample (MLS) intervals by Hernandez and Burdick (1993), a simulation study is conducted. The results indicate that the proposed method performs better than the MLS method, especially for very unbalanced designs.

Keywords:

• Coverage probability
• Generalized pivotal quantity
• Variance component

Mathematics Subject Classification:

• Primary 62F25
• Secondary 62J10

Acknowledgments

The author cordially thanks anonymous referees for their valuable comments which led to the improvement of this paper. This work was partly supported by Grant 10771126 from National Natural Science Foundation of China, and Grant 2006KJZ01 from Shandong Univeristy of Technology.