Dissertation > Mathematical sciences and chemical > Mathematics > Probability Theory and Mathematical Statistics > Mathematical Statistics > General mathematical statistics

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
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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 n-dimensional random vectors can be observed; known array X n × p order; β is a fixed effect, it is a p-dimensional 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 non-negative 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. Two-way 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. Two-way 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. Two-way 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 three-way 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

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