包含多余回归变量的错误指定模型的随机约束Liu估计

On the Stochastic Restricted Liu Estimator under Misspecification due to Inclusion of Some Superfluous Variables

摘要: 对由于包含多余回归自变量而导致的错误指定线性回归模型, 本文导出了回归系数的最小二乘估计, 普通混合估计以及随机约束Liu估计, 并在均方误差矩阵准则下对这三个估计的优良性进行了比较, 给出了随机约束Liu估计优于最小二乘估计和普通混合估计的充要条件. 此外, 对它们所对应的经典预测值的优良性也进行了讨论.

Abstract: In this paper, we firstly derived the expressions of the well-known ordinary least square estimator (OLSE), the ordinary mixed estimator (OME) introduced by Theil and Golberger (1961) and the stochastic restricted Liu estimator (SRLE) proposed by Yang and Xu (2007) under misspecification due to inclusion of some superfluous variables. Then, performances of these estimators under misspecification are examined. In particular, necessary and sufficient conditions for the superiority of the SRLE over the OLSE and OME with respect to the mean squared error matrix (MSEM) criterion are derived. Furthermore, superiority of the corresponding predictors of these estimators are also investigated.