两类线性模型回归系数的平衡LS估计及性质

THE BALANCED LS ESTIMATIONS OF THE REGRESSION COEFFICIENTS FOR TWO KINDS OF LINEAR MODELS AND THEIR PROPERTIES

基于平衡损失的思想，讨论了当误差协方差阵Cov（e）=σ^2∑，其中∑〉0和∑≥0时，两类线性模型回归系数的参数估计问题，提出了新的参数估计标准，分别得到了广义平衡LS估计和奇异平衡LS估计，同时进一步研究了两种估计在不同准则下的优良性，给出了一个应用实例．

Abstract Based on the idea of the balanced loss function, this paper considers two kinds of linear regression models which are subject to Cov（e） =σ^2∑, with ∑ 〉 0 and ∑ ≥ 0, respectively. New standards for estimating the regression coefficients of the two models are proposed, and the general balanced LS estimation and the singular balanced LS estimation are presented. Frthermore, their superior properties with respect to some criteria are analyzed. Finally, a numerical example is provided to illustrate the application of the balanced LS estimation.