Computational Statistics

, Volume 31, Issue 3, pp 973–988 | Cite as

Least squares generalized inferences in unbalanced two-component normal mixed linear model

  • Xuhua LiuEmail author
  • Xingzhong Xu
  • Jan Hannig
Original Paper


In this paper, we make use of least squares idea to construct new fiducial generalized pivotal quantities of variance components in two-component normal mixed linear model, then obtain generalized confidence intervals for two variance components and the ratio of the two variance components. The simulation results demonstrate that the new method performs very well in terms of both empirical coverage probability and average interval length. The newly proposed method also is illustrated by a real data example.


Variance component Least squares Fiducial generalized pivotal quantity Fiducial generalized confidence interval 



Xuhua Liu’s work was supported by the National Natural Science Foundation of China under Grant No. 11201478 and 11471030. Xingzhong Xu’s work was supported by the National Natural Science Foundation of China under Grant No. 11471035. Jan Hannig’s research was supported in part by the National Science Foundation under Grant No. 1016441. The authors are very grateful to the two reviewers for their valuable comments and suggestions on the earlier versions of this paper.

Supplementary material

180_2015_604_MOESM1_ESM.pdf (67 kb)
Supplementary material 1 (pdf 66 KB)


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of MathematicsChina Agricultural UniversityBeijingChina
  2. 2.College of MathematicsBeijing Institute of TechnologyBeijingChina
  3. 3.Department of Statistics and Operations ResearchThe University of North Carolina at Chapel HillChapel HillUSA

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