Bayes estimates of variance components in mixed linear model

Abstract

This paper proves that in mixed linear model, the analysis of variance estimation (ANOVAE), the minimum norm quadratic unbiased estimation (MINQUE), the spectral decomposition estimation (SDE) and the restricted maximum likelihood estimation (RMLE) of variance components are the same under some conditions. Based on this result, we construct a linear Bayes estimation (LBE) for the parameter vector consisting of variance components and establish its superiorities. Numerical computations and an illustration show that the LBE is comparable to Lindley's approximation, Tierney and Kadane's approximation and the usual Bayes estimation (UBE) obtained by the MCMC method and easy to use as well.

Keywords:

• Mixed linear model
• variance components
• linear Bayes procedure

Acknowledgments

We would like to thank the Editor and reviewers for the comments and suggestions, which have improved the presentation and quality of the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Supported by NNSF of China (11371051)