基于LASSO的部分线性单指标模型局部惩罚样条估计

Local Penalty Spline Estimation of LASSO-based Partial Linear Single Index Model

针对部分线性单指标模型,文章构建了一种基于LASSO的部分线性单指标模型局部惩罚样条估计方法,以变异系数作为判断数据离散程度的依据,首先通过计算各节点中数据的变异系数,构造局部惩罚权重矩阵,由局部二次逼近方法,得到了带有LASSO局部惩罚的参数估计值,并讨论得出无惩罚样条估计和均匀惩罚样条估计是局部惩罚样条估计的特殊情况,然后使用"去一分量"法和Levenberg-Marquardt算法得到单指标部分的参数估计值,最后通过Monte-Carlo模拟验证了该方法的有效性和正确性。

For the partial linear single index model, this paper constructs a local penalty spline estimation method of partial linear single index model based on LASSO. The variation coefficient is used as the basis to judge the degree of data dispersion.Firstly, the local penalty weight matrix is constructed by calculating the variation coefficient of the data in each node, and the local quadratic approximation method is used to obtain the parameter estimates with LASSO local penalty, with the conclusion drawn from discussion that non-penalty spline estimation and uniform penalty spline estimation are special cases of local penalty spline estimation. Then, the parameter estimates of single index part are obtained by"de-one component"method and Levenberg-Marquardt algorithm. Finally, the validity and correctness of the proposed method are verified by Monte Carlo simulation.