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.
[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.
[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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:71720", author = "Shuimiao Wan and Chao Yuan and Baoguang Tian", title = "An Estimation of Variance Components in Linear Mixed Model", abstract = "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.", keywords = "Linear mixed model, Random effects, Parameter
estimation, Stein function.", volume = "9", number = "12", pages = "741-4", }