函数型分位数回归的局部稀疏估计方法

A Local Sparse Estimation Method of Functional Quantile Regression

文章针对协变量为函数型变量、响应变量为标量的函数型分位数回归模型,提出了一种局部稀疏估计方法,能够正确识别系数函数的空子区域。首先,使用非对称拉普拉斯分布构建函数型分位数回归的全似然函数,并通过EM算法推导出系数向量的估计式。其次,提出了一种结合样条光滑和平滑剪切绝对偏离方法的局部稀疏估计方法。数值模拟结果表明,该估计方法在不同的样本量和分位点下均优于传统方法。最后,通过实例证明了估计方法的有效性。

This paper proposes a local sparse estimation method for functional quantile regression models that include functional covariates and scalar response variables.This method can be used to effectively identify vacant subintervals of coefficient functions.Firstly,the full likelihood function of function quantile regression is constructed by using asymmetric Laplacian distribution,and the estimator of coefficient vector is derived by EM algorithm.Secondly,a local sparse estimation method is proposed based on spline smoothing and smooth shear absolute deviation method.Numerical simulation results show that the estimation method is superior to traditional methods in different sample sizes and quantiles.Finally,an example is given to verify the effectiveness of the estimation method.