从约束型最小二乘估计到约束型岭估计的探索

Exploration on the Restricted Least Squares Estimation to the Restricted Ridge Estimation

考虑非齐次约束线性回归模型回归系数的最小二乘估计及岭估计,当设计阵X为病态时,最小二乘估计不再是一个优良估计,提出了一种约束型岭估计,从约束条件入手,借助条件极值法研究(Y-Xβ)′(Y-Xβ)的最小值,使问题转化为在两个约束条件下的优化问题。

We considered the least squares estimation and the ridge estimation of regression coefficient in the heterogeneous restricted linear regression model. When the design matrix X is all ill-conditioned matrix, the least squares estimation is no longer a good estimation, The paper proposes a new restricted ridge estimation, obtains from the restricted condition, with the aid of condition extreme Value, we study the minimization of （Y-X β）＇ （Y-X β）,and cause the question to transform as optimized question under two restricted conditions.