关于线性回归模型的有偏估计

有偏估计方法是近代回归分析的常用方法．本文研究了几种常用的有偏估计方法，澄清了这些方法的区别和联系．对有偏估计的一些关键点进行研究，给出了一种新的岭参数确定法和一种新的主成分概念，并讨论了这些方法的优良性．为了提高有偏估计的效率，提出了用比例因子规范模型的方法．最后，给出了说明本文方法的数值例子．

ON BIASED ESTIMATE METHODS FOR LINEAR REGRESSION MODELS

Biased estimate methods are basic methods of modern regression analysis.In this paper,we study the usual biased estimate methods,discover their relationship and distinct features.We deal with the key problems to biased estimate methods, present a new concept of principal components and a new method to determine ridge parameters;simultaneously,we prove the methods'good properties.For increasing the efficiency of biased estimate methods,we present a method of normalizing models by ratio scales.Finally,we give numerical examples to illustrate our methods.