基于垂直距离的回归方法

REGRESSION ANALYSIS BASED ON DISTANCE

本文介绍基于垂直距离的回归分析方法。在距离回归中,y对x以及x对y的回归都对应着同一根直线,由于自变量与因变量在距离回归方程中地位对等,使变量数值之间的相互转换十分方便,特别适用于自变量与因变量都同时含有误差的情形。显然这比经典回归方法更符合应用的实际情形。本文将介绍距离回归的模型、解法、算法,也介绍它与经典回归、主成分分析以及特征根回归之间的关系.

In this paper, the authors discuss linear regression method based on vertical distance. In the equation of distance regression the response variable y and independent variable x are equal in status, the regression of y on x or the regression of % on y coresponds to the same regression line. This method can be used for quantitative transformation of variables each other. It is more efficient than the classical regression if both the response variable y and independent variable x contain error. The authors also show its relationship to principal component, classical regression and latent root regression (Webster 1974).