响应变量随机缺失下线性回归模型的自适应期望递归最小二乘算法

在响应变量随机缺失MAR机制的前提条件下, 针对线性回归模型,提出了一个新的期望递归最小二乘算法(Expectation Recursive LeastSquare, ERLS), ERLS方法巧妙的结合了EM算法和RLS的优点,自适应的递归估计回归系数, 从而避免了高维数据的相关矩阵的求逆困难.ERLS算法是实时自适应处理算法, 无需存储全部数据集,在观测数据存在野值时, ERLS算法优于LS方法.

ERLS Algorithm for Linear Regression Model with Missing Response Variable

A novel Expectation Least Square(ERLS) algorithm is proposed for linear regression model.Under the condition that response is partly missing,ERLS uses expectation value of the response instead of the missing value.Based on the expectation value and the data of independent variable,ERLS adaptively estimates the regression coefficients,which avoids the difficulty of inversion operation to the correlation matrix of high-dimensional data.ERLS makes fully use of the available data and sovles the regression problem in an online manner.Numerical expriments show that,by introducing a nonlinear function of supression,ERLS is superior to LS solution under the existence of wild data points.