Linear Admissible Estimators And Minimax Estimators Of Regression Coefficient Matrix In Restricted Growth Curve Model

Different estimations of regression coefficients matrix B were discussed in many documents, especially the least square estimate. And there have been rather mature theories about the admissibility of general growth curve model parameter estimation. These researches were spread in the homogeneous admissible estimators and the inhomogeneous admissible estimators under a non-restricted condition. But in many cases, due to the prior knowledge of the parameters, some restricted requirements are met by the parameters. So, great importance is attached to study the estimation of the growth curve model parameters with restricted condition.This paper studies the growth curve model under the homogeneous restricted conditionIn the model(1),X₁, X₂ and Hare known design matrix of n×k, p×q, l×k order,σ² and B_k×q are unknown parameters,(?) is straightenedvectors ofε, V (?)∑denotes the Kronecker product of V and∑. andIn the model(2), Y_i,ε_i are n×p order matrix,σ² and B_k×q are unknown parameters, (?) is straightened vectors ofε_i,σ² =(σ₁²,σ₂²,…σ_m²), V(?)∑denotes the Kronecker product of V and∑.Firstly, it can be concluded that the estimable function KBL is the sufficiency and necessity conditions of admissible Minimax estimation under the homogeneous admissible estimators L₀ and inhomogeneous admissible estimators L₁ in terms of model (1) and matrix loss.Secondly, we studied the linear admissible estimators and linear admissible Minimax estimators of linear estimable function KBL in growth curve model with common mean parameter under model (2) and quadric loss, and the sufficiency and necessity conditions of linear admissible Minimax estimation in the two linear admissible L₀ and L₁ are calculated.