Variance component model fixed effects estimates 

Author  FangLiBao 
Tutor  ChenGuiJing 
School  Anhui University 
Course  Mathematical Statistics 
Keywords  Variance component model Fixed effects Linear minimax estimates Mixed linear model Maximum likelihood estimation Interaction effects Hybrid model Unknown parameter vector Observable Least squares estimation 
CLC  O212.1 
Type  Master's thesis 
Year  2002 
Downloads  120 
Quotes  0 
The the considering mixed linear model Y = Xβ _{ U 1 ξ 1 ... } U _{ k } ξ _{ k }, E (ξ _{ i }) = 0, i = 1,2, ..., cov (ξ _{ i }, ξ _{ j }) = 0 , i ≠ j, cov (ξ _{ i }, ξ _{ i })σ _{ i } ^{ 2 V i , i, j = 1,2, ... k. Wherein: Y is ndimensional random vectors can be observed; known array X n × p order; β is a fixed effect, it is a pdimensional unknown parameter vector; ξ i is unobservable t < sub> i dimensional random vector; U i is the n × t i order known array; V i is the n × n order nonnegative definite known array . 2 ≥ 0 for unknown parameters σ i, i = 1, 2, ..., and k. Firstly, given the mixed linear fixed effects model, maximum likelihood estimation, and then give a linear minimax estimated. The unidirectional classification the random model y ij = μ the aie ij j = 1,2, ..., b where μ is the fixed effect, for a i random effects. Twoway classification mixed the model y ij = μ the a i β j e ij i = 1,2, ... a, b = 1,2, ..., 6 where μ, a i is a fixed effect, β j is a random effect. Twoway classification random model (no interaction) y ij = μ ai β j e ij i = 1,2, ..., a j = 1,2, ..., b where μ is the fixed effect, a i , β j random effects. Twoway classification random model (interaction effects) y ijk = μ the a i β j the γ ij e < sub> ijk i = 1,2, ..., a, j = 1,2, ..., b, k = 1,2, ..., c where μ is a fixed effect, the A i , the β j the γ ij are random threeway classification random effects model (without interaction) y ijk = μ i β j γ k e ijk i = 1,2, ..., a, j = 1,2, ..., b, k = 1,2, ..., c where μ is the fixed effect, a i , β j , γ k are random effects . The two sets of classification model plant fixed effects, n, pj doors are random effects. These fixed effects model maximum likelihood estimation is least squares estimation. The hybrid model, considering its linear estimable function Sg estimated the LY, select the loss function Bingjia c; two foot. set risk function nZn Theorem 1 RSg is estimated to be only linear minimax }