因变量缺失下线性回归模型的约束岭估计

Restricted Ridge Estimation of Linear Regression Model with Missing Responses

摘要: 本文考虑线性回归模型在因变量存在缺失且回归系数存在线性约束下的岭估计，分别基于完整数据方法和单一插补方法，构造了回归系数的约束岭估计，解决了线性回归模型在因变量缺失、自变量存在多重共线性和回归系数存在线性约束这三种情况同时存在情形下的估计问题，给出了所提估计量的渐近性质。最后通过数值模拟验证了所提方法的有效性。

Abstract: This paper addresses ridge estimation in linear regression models when the dependent variable has missing values and the regression coefficients are subject to linear restrictions. Based on the complete data method and single imputation method, the corresponding restricted ridge estimators for the regression coefficients are constructed. This approach resolves the estimation problem in linear regression models when three conditions coexist: missing dependent variables, multicollinearity, and linear restriction on regression coefficients. The asymptotic properties of the proposed estimators are given. Finally, some simulations are conducted to illustrate the proposed methods.