An Estimation of Variance Components in Linear Mixed Model

In this paper, a linear mixed model which has two random effects is broken up into two models. This thesis gets the parameter estimation of the original model and an estimation’s statistical qualities based on these two models. Then many important properties are given by comparing this estimation with other general estimations. At the same time, this paper proves the analysis of variance estimate (ANOVAE) about σ2 of the original model is equal to the least-squares estimation (LSE) about σ2 of these two models. Finally, it also proves that this estimation is better than ANOVAE under Stein function and special condition in some degree.

Authors:

• Shuimiao Wan
• Chao Yuan
• Baoguang Tian

Keywords:

• Linear mixed model
• Random effects
• Parameter estimation
• Stein function.

References:

[1] W.L. Xu. A estimation of variance component in linear mixed model (J).
Applied probability and statistics, 2009, 25(3), pp.301-308.
[2] S.G. Wang, J.H. Shi, S.J. Yin. Linear model introduction (M).Beijing
science press. 2004.
[3] Y.H. Fan, S.G. Wang. The improvement about ANOVAE of variance
component in linear mixed model (J). Applied mathematics A journal of
Chinese universities, 2007, 22(1), pp.67-73.
[4] M.X. Wu, S.G. Wang. The optimal estimation about fixed effect and
variance component simultaneously (J). Chinese science ser.A, 2004,
15(3):3732384.
[5] K. Tatsuga. Estimation of variance components in mixed linear models
(J). Journal of multivatiate analysis, 1995, 53:2102236.
[6] L.R. Lamotte. One non-negative quadratic unbiased estimation of
variance components (J). Journal of the american statistical association,
1973, 68, pp.728-730.
[7] J.H. Shi, S.G. Wang. A non-negative estimation of variance component
(J). Chinese journal of engineering mathematics, 2004, 21(4):6232627.
[8] X.R. Chen. Statistics introduction. Beijing Science Press, 1981,
pp.104-108.