线性模型的泛最小二乘法

Universal least squares method of a linear model

本文首先针对线性模型提出了泛最小二乘法,在设计矩阵不加限制的情形下,得到了参数的泛最小二乘估计量。该方法既发扬了最小二乘法的优点,又克服了它的一些不足,它包含了常见的岭估计和最小二乘估计法;其次讨论了泛最小二乘法的理论依据;接着研究了泛最小二乘估计量的一些统计性质,并与最小二乘估计进行比较,在一定意义上前者优于后者;然后讨论了平衡参数的选取问题;最后,给出一个应用,说明了泛最小二乘法的有效性和可行性。

Firstly, the universal least squares method for the linear model is given in this paper, and the parametric estimator is attained without a restrained design matrix. The method not only holds the virtues of least squares method, but also overcomes its some deficiencies, and the method contains ridge estimate and least squares estimate method. Secondly, theoretical foundation of the universal least squares method is investigated. Thirdly, some statistical properties of universal least squares estimators are discussed, at the same time, the universal least squares estimation is compared with the least squares estimation, and the conclusion is that the former excels the latter. Fourthly, the matter of choosing balance parameter is researched. Finally, the validity and feasibility＂ of the method are illustrated by＂ an application.