基于惩罚极大Lq似然的Logistic回归系数的估计及变量选择

Estimation and Variable Selection of Logistic Regression Coefficient Based on Penalizing Maximum Lq Likelihood

极大似然估计是Logistic回归模型的常用参数估计方法,且在一定条件下具有一致性和渐近正态性。但极大似然估计的优良性主要体现在大样本情况,当解释变量具有多重共线性且样本量较小时,为得到更好的拟合效果以及实现参数稀疏化,将极大Lq似然估计与Lasso惩罚结合,得到Lasso极大Lq似然估计。并运用数值模拟对Lasso极大似然估计和Lasso极大Lq似然估计进行比较得到,在样本量较小时,Lasso极大Lq似然估计的表现优于Lasso极大似然估计。

Maximum likelihood estimation is a commonly used parameter estimation method of Logistic regression model,and it has consistency and asymptotic normality under certain conditions.However,the superiority of maximum likelihood estimation is mainly reflected in the case of large samples.When explanatory variables have multicollinearity and the sample size is small,in order to obtain a better fitting effect and achieve parameter sparseness,the maximum Lq likelihood estimation is combined with the Lasso penalty to obtain the Lasso maximum Lq likelihood estimation.And numerical simulation is used to compare the Lasso maximum likelihood estimation and Lasso maximum Lq likelihood estimation.The results show when the sample size is small,the performance of Lasso maximum Lq likelihood estimation is better than Lasso maximum likelihood estimation.