两线性随机效应模型未知参数函数预测量的等价性研究

Equivalence Study of Unknown Parameter Function Predictors under Two Linear Random Effects Models

摘要: 假设对一般线性随机效应模型添加新的变量项成为过参数线性随机效应模型，这时两模型相同未知参数的统计推断不一定相同。针对这一问题，本文利用带约束限制二次矩阵值函数最优化问题的解，给出过参数线性随机效应模型下未知参数函数的最佳线性无偏预测/最佳线性无偏估计的解析表达式，并利用一些代数与矩阵理论工具，得到了两模型未知参数函数最佳线性无偏预测/最佳线性无偏估计等价的条件。

Abstract: Suppose that adding a new variable term to the general linear random-effect model becomes the overparameter linear random-effect model, then the statistical inference of the some unknown parameter of the two models is not necessarily the same. In order to solve this problem, this paper uses the solution of constrained quadratic matrix-valued function optimization problem to give the analytical expression of the best linear unbiased predictor/best linear unbiased estimator of the unknown parameter function under the overparameter linear random-effect model. The conditions for the equivalence of the best linear unbiased predictor/best linear unbiased estimator of unknown parameter functions of two models are obtained by using some algebra and matrix theory tools.